WEBVTT

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Is it working for them?

2
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And keep telling me about stuff like that, thank you, because I can't always.

3
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We can see and hear you.

4
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Thanks Ryan yeah.

5
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And naturally.

6
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Good okay.

7
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Okay.

8
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Hello.

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Barry.

10
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Binomial.

11
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Probably bill in times probability of K head we don't care. The order is.

12
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Okay.

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And fees the probability of any 1 going being ahead.

14
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Okay, so expected value definition is the sum of all the K.

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Hey, so it did this last time to review it.

16
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Huh.

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Okay, and then I got pull out the case and I can pull out a p, and I can do this. It was then pay some of all the.

18
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So, I pulled out an in from the in fact, -1 is the case here.

19
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I'll pull out a piece, so this will be Peter. The K -1.

20
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And the, the, and minus K Victoria.

21
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Um, the case will be.

22
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And that will be in page. Some of all the.

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And -1 two's K -1.

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And this thing here.

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1.

26
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So he goes then pay.

27
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There just a quick review and now I'm skipping over things like the limit what happens with 0 and solid. It all works out correctly.

28
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Let me write that down. This is a reviewed.

29
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Okay.

30
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Okay.

31
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Hello.

32
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Mm, hmm.

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Over.

34
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Is, um.

35
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You know, the again cases.

36
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Okay, 0, etc. However they do a workout.

37
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Hello.

38
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It didn't work out, so okay, so.

39
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Now, the variance okay, by definition is expected value of case where.

40
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Expected value. Okay. Where.

41
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Now, expected values that so the expected value of case squared.

42
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So, um.

43
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Hey, squared equals K times 1-K times 8-1.

44
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Okay, okay so.

45
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Value in the case squared is expected the value of K. K. -1.

46
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Value K, which I know that.

47
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Um, so.

48
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The reason I, I did this here is well, it works out.

49
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Okay, so this thing here.

50
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Equal for some of all the.

51
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8 times K -1.

52
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5. K. K. minus P.

53
00:05:12.178 --> 00:05:17.459
Okay, okay so that, um.

54
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Equals I'm going to do about 2 things at once. I'm going to pull in times and -1 here.

55
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And so we and -2 factorial.

56
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And the K factorial, this will be a K -2 factorial.

57
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And the, and minus K Victoria will be the same.

58
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And I'm going to pull up 2 piece of.

59
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Where, and this will be a P2 the K -2.

60
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1, to the end minus. Okay.

61
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Okay, so I did 3 or 4 things in that 1 line. So.

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I'll leave it up and let people think about that was going from here to here.

63
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So, if it's confusing, I can split it and do it as 4 separate lives. Just speak up.

64
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And you do that um, let me do that anyway. Um, I've got to feel this may be confusing.

65
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Hello.

66
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Okay, um.

67
00:06:26.038 --> 00:06:32.519
Okay, so what I have is I have the sum of all the K. K. -1.

68
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This is expected value K. K. -1.

69
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Because there's times and.

70
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Got it.

71
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Okay, I'm equals.

72
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In factorial over K factorial and.

73
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Okay, now.

74
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We came up to the factory. Okay.

75
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So, that equal, some of all the.

76
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Hello.

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Okay, now the next thing is that, um.

78
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And I'm going to pull out this work on this thing here.

79
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And I'm going to get and times and -1 time to some of those.

80
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It's too factorial, blah, blah, blah, blah, blah, blah, blah, blah.

81
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Okay, and tutorials and timezone -1 times I understood factorial.

82
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Um.

83
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And this thing here is going to be P square feet of the K -2 that was okay up there.

84
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Okay, I'm going to pull the whole thing.

85
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So, that's how I'm pulling stuff down the department.

86
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So.

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Hello.

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Huh.

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Right.

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Tell me.

91
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Hello.

92
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Huh.

93
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Okay, so I'm going to take this and pull out the P and know what I'll do is.

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Closed.

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Clear.

96
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Some of the -2 factorial.

97
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Hey.

98
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Totally. Okay. Victoria.

99
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To hey.

100
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And this here, nothing on the right is a solid and -2 K to choose.

101
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Feet of the K -1-P.

102
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Okay, and.

103
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Weird and this thing here is 1.

104
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So, the whole thing.

105
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Equal and this is expected value of K. K.

106
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-1 it goes then comes then -1 time piece where.

107
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Okay, so so the expected value of the case squared.

108
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Is this thing -1.

109
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Plus expected value. Okay.

110
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And then -1 square.

111
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Okay, okay.

112
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I'm not sure I screwed up. Okay.

113
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Other than.

114
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Okay, so.

115
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The variance was insufficient value case squared minus value. Okay.

116
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Where it was the previous thing.

117
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Hello.

118
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I know.

119
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Where.

120
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Okay, which we can simplify as, um.

121
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P squared .

122
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N. P. squared plus minus for Q squared.

123
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And keep in mind.

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Squared because.

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Go on.

126
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Okay.

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Equal and G1 line, it's.

128
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Input and.

129
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Really.

130
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And so, let me give you some examples here.

131
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But what does the variants some shortcuts? Basically some abbreviations.

132
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Um.

133
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Um, we use new to be the expected value.

134
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Sigma where it could be the various.

135
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Segment to be the deviation of the variance.

136
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Okay, some you and think about their common things.

137
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Because me is the Greek asthma that's for me and segments the Greek gas. Okay.

138
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Um, now.

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Hello.

140
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And again, if I scroll up too fast shout out, so roughly.

141
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The probability of any random variable that.

142
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New minus think my less than equal to K less than 2.

143
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You plus a Sigma equals 2 thirds.

144
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Roughly, okay, probabilty that is.

145
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Greater than equal to plus segment. 6.

146
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Probably okay.

147
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Okay, so let's see an application.

148
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Coin 100 times. Fair coin. Okay. Okay.

149
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I can do.

150
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Unfair coins also, but just make it easier. Okay, so, and equals 100.

151
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Vehicles 1, half the main is an equal 50.

152
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The Sigma squared is 2 is also 1 half. Okay.

153
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Equal 25.

154
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So, 6, 5.

155
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So so 2 thirds of the time.

156
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The number of head.

157
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Is 15+or -5.

158
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Hello.

159
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Now, leave this up for a 2nd, it's application of energy.

160
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Or we could say that also as, you know.

161
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50+or minus plus or -10%you could say, okay.

162
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But, you know, the meeting with the 10% of the.

163
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Okay.

164
00:16:05.788 --> 00:16:09.509
Now, as we tossed the coin more and more times.

165
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The number of heads, it gets tighter.

166
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It doesn't spread out as much so, um.

167
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You.

168
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Let's say 5 times.

169
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25 times let's say, 8+25 P equals 1 half.

170
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The mean is, um.

171
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And a half, the segment clarity equals.

172
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25 quarters those Sigma.

173
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Cool. I have so, 2 thirds of the time.

174
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Number of head.

175
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Is and a half plus or .

176
00:17:15.419 --> 00:17:19.979
And this is 20 or.

177
00:17:19.979 --> 00:17:25.558
So, if we talked about 25 times.

178
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Then we're within 2 thirds of the time we're within 20% of the me.

179
00:17:31.769 --> 00:17:37.499
If we toss it 100 times, 2 thirds of the time, we're within 10% of the mean.

180
00:17:37.499 --> 00:17:42.749
So that's, um.

181
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10,000 times and equals 10,000.

182
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We close 1 half the mean is 5,000.

183
00:17:54.509 --> 00:17:58.259
The segment will actually be 50.

184
00:17:59.519 --> 00:18:02.939
So, 2 thirds of the time, it will be 5,000.

185
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Plus or -50which is plus or -1%.

186
00:18:07.858 --> 00:18:15.179
So the relative spread gets a lot less the more time to tossed the coin. It's like a large number of.

187
00:18:15.179 --> 00:18:26.759
That's the left, so I computed the form the formula for the variance of binomial distribution and I.

188
00:18:27.898 --> 00:18:33.118
Then show you that, as you talk to the coin more time, because it's more and more tightly cluster.

189
00:18:33.118 --> 00:18:36.148
Relatively speaking, it was affected.

190
00:18:36.148 --> 00:18:40.739
Okay.

191
00:18:43.348 --> 00:18:46.798
Let me do a geometric distribution now.

192
00:18:46.798 --> 00:18:51.449
So, it will show you a different techniques here.

193
00:18:51.449 --> 00:18:57.479
So, we talked we tossed the coin the random variable.

194
00:18:57.479 --> 00:19:01.709
Is, what's the number of the 1st cost that gives me a hand okay.

195
00:19:03.689 --> 00:19:07.919
And variable is the cost number.

196
00:19:10.378 --> 00:19:15.148
That gives you.

197
00:19:16.528 --> 00:19:20.308
Okay, and if he is the probability.

198
00:19:22.828 --> 00:19:26.519
That 1 cost.

199
00:19:26.519 --> 00:19:33.959
Goes ahead and all of these fine points where something there on correlated blah, blah, blah, blah.

200
00:19:33.959 --> 00:19:37.138
The probability of the 1st cost is on a K.

201
00:19:37.138 --> 00:19:43.828
Is, um, this was the head and 1-B.

202
00:19:43.828 --> 00:19:47.249
For the K, -1 all the others were tail.

203
00:19:47.249 --> 00:19:54.419
Okay, um, and I might use cube sometimes. I'll also.

204
00:19:56.128 --> 00:20:00.808
Expected value K and K greater or equal to 1.

205
00:20:04.199 --> 00:20:09.209
And it's countably infinite. Okay. Right?

206
00:20:09.209 --> 00:20:18.088
Okay, okay now.

207
00:20:18.088 --> 00:20:21.479
The expected value did before.

208
00:20:23.669 --> 00:20:28.679
Okay, it goes 1 to infinity many times to be. Okay.

209
00:20:28.679 --> 00:20:32.368
It goes to some of all the K.

210
00:20:32.368 --> 00:20:36.689
For the P1-P to the case.

211
00:20:36.689 --> 00:20:41.159
1, so how do we do that there? Okay so.

212
00:20:41.159 --> 00:20:47.699
Okay.

213
00:20:50.909 --> 00:20:54.419
Um.

214
00:20:55.888 --> 00:20:59.009
Let me go to the next page, um.

215
00:21:03.509 --> 00:21:08.729
Okay, um, actually what I want.

216
00:21:08.729 --> 00:21:14.249
Some of all the K1.

217
00:21:14.249 --> 00:21:20.189
And well, what I come on the 2nd, here there, we go.

218
00:21:20.189 --> 00:21:26.548
Well, um, I can do it like this, um.

219
00:21:30.028 --> 00:21:33.419
Some of all the due to the K.

220
00:21:33.419 --> 00:21:39.118
80 to infinity equals 1 over 1.

221
00:21:39.118 --> 00:21:43.528
It's the formation of a geometric series.

222
00:21:43.528 --> 00:21:47.009
So.

223
00:21:47.009 --> 00:21:50.429
Let me, let me do derivatives.

224
00:21:55.078 --> 00:21:59.729
So, if I do derivative with respect to queue.

225
00:21:59.729 --> 00:22:05.548
Okay of the left hand side.

226
00:22:05.548 --> 00:22:10.588
Hey, close to some of all the okay fine. That's fine. Okay.

227
00:22:10.588 --> 00:22:15.479
The right hand side, you.

228
00:22:15.479 --> 00:22:21.058
Over the board with the form I want is.

229
00:22:21.058 --> 00:22:24.659
What do I do?

230
00:22:24.659 --> 00:22:31.288
The derivative the 1-to, the -1.

231
00:22:31.288 --> 00:22:35.249
It's going to be 2 times 1-2 to the -2.

232
00:22:35.249 --> 00:22:39.719
The -1 goes down to -2 for -1 in front.

233
00:22:39.719 --> 00:22:43.108
And the .

234
00:22:43.108 --> 00:22:48.419
Okay, 1-queue to the -2.

235
00:22:48.419 --> 00:22:52.318
Okay, so.

236
00:22:52.318 --> 00:22:56.969
But we have is the, the sum of all the.

237
00:22:56.969 --> 00:23:00.568
Hey, go to the K -1.

238
00:23:00.568 --> 00:23:03.628
Equals 1-queue to the minus to.

239
00:23:03.628 --> 00:23:08.098
Okay, so.

240
00:23:08.098 --> 00:23:11.669
Um.

241
00:23:11.669 --> 00:23:15.239
So, they expected value.

242
00:23:15.239 --> 00:23:18.358
Okay, which was.

243
00:23:18.358 --> 00:23:22.769
Some of all the K. D. K. -1.

244
00:23:22.769 --> 00:23:27.058
Was was that P times, um.

245
00:23:27.058 --> 00:23:30.328
1-2 the -2.

246
00:23:30.328 --> 00:23:34.949
Which, and 1-which is 1 over.

247
00:23:36.628 --> 00:23:40.439
So.

248
00:23:40.439 --> 00:23:45.838
So, fair coin equals 1.

249
00:23:45.838 --> 00:23:51.538
So, probably a cake was 1 of a head on the 1st cost is 1 half.

250
00:23:51.538 --> 00:23:55.288
Oh, equals 2 is 1 quarter.

251
00:23:55.288 --> 00:23:58.858
Okay, 3 408.

252
00:23:58.858 --> 00:24:02.909
So, on expected value okay.

253
00:24:02.909 --> 00:24:07.439
April 2 on the average, the 2nd thing. Okay. So.

254
00:24:07.439 --> 00:24:14.489
See, how the computer expected value. Okay variant do gets a little weirder.

255
00:24:15.749 --> 00:24:22.979
Um, if I scrolled too quickly, then, um.

256
00:24:24.568 --> 00:24:28.169
Hello.

257
00:24:35.308 --> 00:24:38.909
All right.

258
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Now, oops, very.

259
00:24:49.469 --> 00:24:55.199
Again, expected value of case where invited.

260
00:24:55.199 --> 00:25:04.048
Okay, and for case square it again, I'm going to do case square equals. Kay Kay.

261
00:25:04.048 --> 00:25:08.699
Fine this 1. okay. Okay. Um.

262
00:25:08.699 --> 00:25:15.419
Now, what I had before was I had the sum of all the.

263
00:25:15.419 --> 00:25:21.419
K time due to the K minus squad equals 1-to.

264
00:25:21.419 --> 00:25:26.308
To get that, right? Yeah. Okay.

265
00:25:28.558 --> 00:25:32.608
Okay.

266
00:25:32.608 --> 00:25:37.648
So, I'm going to do derivatives again.

267
00:25:37.648 --> 00:25:41.459
Is it again?

268
00:25:41.459 --> 00:25:45.328
So that's the reason we're doing showing you a technique.

269
00:25:45.328 --> 00:25:50.489
Okay, so the thing on the left, we will have UK.

270
00:25:50.489 --> 00:25:53.999
On the left will be the sum of all the K time.

271
00:25:53.999 --> 00:25:58.199
Okay, -12 to the K -2.

272
00:25:58.199 --> 00:26:05.548
On the right it will become 2 times 1-cube to the -3.

273
00:26:07.288 --> 00:26:10.318
Right. Okay.

274
00:26:12.028 --> 00:26:15.028
So.

275
00:26:15.028 --> 00:26:18.989
Hello.

276
00:26:20.368 --> 00:26:24.719
And then what I've got to do is put the thing on the.

277
00:26:24.719 --> 00:26:29.818
Left so what I want to do is put a Q squared on both sides.

278
00:26:31.318 --> 00:26:38.729
And so some of all the K K -1 uses the K.

279
00:26:38.729 --> 00:26:42.749
A called, um.

280
00:26:45.689 --> 00:26:49.259
Actually.

281
00:26:49.259 --> 00:26:55.769
Um.

282
00:26:55.769 --> 00:26:59.999
I actually need to be, um.

283
00:26:59.999 --> 00:27:07.739
Well, the derivation for Q is the same as the derivation for Pete. So actually, some of all the K. K.

284
00:27:07.739 --> 00:27:11.128
K minus what Peter K is going to be.

285
00:27:11.128 --> 00:27:14.548
Square 1.

286
00:27:14.548 --> 00:27:18.179
Okay, and that.

287
00:27:19.558 --> 00:27:25.078
That's the expected value. Okay. -1.

288
00:27:26.159 --> 00:27:33.449
Okay, and I'm going to simplify because this will be to C squared.

289
00:27:33.449 --> 00:27:38.098
Um, that's great.

290
00:27:38.098 --> 00:27:42.209
That's great. Okay.

291
00:27:43.769 --> 00:27:50.278
The various will be the expected value. Okay. K -1.

292
00:27:52.439 --> 00:27:57.959
Plus the expected value K minus expected value of the kidney where.

293
00:27:57.959 --> 00:28:07.499
Expected value of K was 1 over a p.

294
00:28:10.229 --> 00:28:14.548
1, over P .

295
00:28:14.548 --> 00:28:21.509
Where, okay now, did I go to this right? Or did I screw it up?

296
00:28:21.509 --> 00:28:27.659
Um.

297
00:28:27.659 --> 00:28:32.368
I'm going to.

298
00:28:39.868 --> 00:28:43.919
Piece quarter.

299
00:28:43.919 --> 00:28:49.288
Honestly, don't know if it's very helpful. I'm going to pull out a P1 over T Square.

300
00:28:51.538 --> 00:28:55.979
Hello.

301
00:28:57.209 --> 00:29:03.479
Hello.

302
00:29:05.848 --> 00:29:11.429
Call.

303
00:29:15.148 --> 00:29:19.618
Huh.

304
00:29:19.618 --> 00:29:33.358
Let's see what we got here.

305
00:29:33.358 --> 00:29:37.019
Hmm.

306
00:29:37.019 --> 00:29:43.199
I'm going to rewrite pieces 1-so 1-2 of the.

307
00:29:47.489 --> 00:29:53.638
Calls.

308
00:29:57.568 --> 00:30:03.148
Whatever.

309
00:30:05.969 --> 00:30:13.288
Okay.

310
00:30:15.298 --> 00:30:20.878
Okay.

311
00:30:22.288 --> 00:30:27.058
Okay.

312
00:30:32.878 --> 00:30:36.148
Hello.

313
00:30:46.499 --> 00:30:51.088
Hello.

314
00:30:52.618 --> 00:30:56.939
I, I'll continue this on Thursday. I going to ask.

315
00:31:00.028 --> 00:31:09.118
I'll go to nasty theory. I, maybe I'm wrong. Maybe I'm wrong. I don't want to take more of your time, but that's how we basically think how we would find variance.

316
00:31:09.118 --> 00:31:13.888
For this get metrics here, I'll double check my work.

317
00:31:15.419 --> 00:31:19.348
Um.

318
00:31:21.209 --> 00:31:27.898
Next thing that we can do is some conditional expected values of various systems.

319
00:31:29.128 --> 00:31:34.169
Additional stuff, um.

320
00:31:35.608 --> 00:31:40.409
So, let's say the factory.

321
00:31:41.638 --> 00:31:45.659
So, high quality.

322
00:31:47.548 --> 00:31:51.509
And low quality parts.

323
00:31:51.509 --> 00:31:55.469
Okay, so.

324
00:31:55.469 --> 00:31:59.338
The alpha is the probability of a high quality part.

325
00:32:00.659 --> 00:32:04.288
1-alpha the probability of the low quality.

326
00:32:06.148 --> 00:32:09.209
And both type.

327
00:32:11.759 --> 00:32:14.759
The lifetime is geometric.

328
00:32:16.259 --> 00:32:23.038
So that.

329
00:32:24.298 --> 00:32:27.659
For example, for the high quality 1.

330
00:32:29.548 --> 00:32:33.419
Probably in the last K is.

331
00:32:39.209 --> 00:32:44.038
It's our time 1-R to the K -1.

332
00:32:44.038 --> 00:32:47.759
The expected value. Okay. Are.

333
00:32:48.868 --> 00:32:53.338
Low quality yes yes.

334
00:32:53.338 --> 00:32:58.318
Check your value.

335
00:32:59.368 --> 00:33:09.659
So, the assumption is that, for the high quality ones are less than.

336
00:33:09.659 --> 00:33:12.898
So, okay now.

337
00:33:14.788 --> 00:33:21.058
We can start to leave this up for a 2nd and this is I'm working with you. An example.

338
00:33:21.058 --> 00:33:25.348
Oh.

339
00:33:30.328 --> 00:33:34.528
You know, I've been thinking what I really need to bring with me are 3 computers.

340
00:33:34.528 --> 00:33:40.618
You know, 1, computer to run Webex the 2nd computer to write the notes on and the 3rd computer to refer to.

341
00:33:40.618 --> 00:33:44.128
But maybe I'll start for the Pre computers to class.

342
00:33:44.128 --> 00:33:49.108
Okay, so.

343
00:33:49.108 --> 00:33:53.608
Hello.

344
00:33:53.608 --> 00:33:56.939
So, basically, so what.

345
00:33:56.939 --> 00:34:00.269
Expected value of K.

346
00:34:02.729 --> 00:34:07.169
Um.

347
00:34:07.169 --> 00:34:11.548
No, no, no part.

348
00:34:14.938 --> 00:34:20.849
So expected value K, we can use conditional things. So that is expected value.

349
00:34:20.849 --> 00:34:27.539
Okay, given given a high quality part.

350
00:34:27.539 --> 00:34:31.829
And the probability of a high part.

351
00:34:31.829 --> 00:34:35.878
So, it's expected value of K, given us the low quality part.

352
00:34:35.878 --> 00:34:40.438
The local part, so.

353
00:34:40.438 --> 00:34:45.838
Went over our times alpha +1 overhead.

354
00:34:45.838 --> 00:34:49.648
Hello.

355
00:34:49.648 --> 00:34:53.219
We couldn't do it along with that.

356
00:34:53.219 --> 00:34:56.338
But also variances.

357
00:34:59.039 --> 00:35:02.398
From the expected value of okay.

358
00:35:02.398 --> 00:35:16.498
Where I'll walk you through this, a started expect value case squared would be the expected value of case where it given the high quality part.

359
00:35:16.498 --> 00:35:19.949
The probability of high, which will be alpha.

360
00:35:23.608 --> 00:35:28.619
Plus the expected value of case where, um.

361
00:35:32.398 --> 00:35:37.259
Plus the expected value of case where it's a low quality part in times 1.

362
00:35:37.259 --> 00:35:41.579
And you can use that you can work out the variance from there. Oh.

363
00:35:44.039 --> 00:35:47.998
Very good to be continuing the script, man. Yeah.

364
00:35:47.998 --> 00:35:51.059
But we could do something like that. Um.

365
00:35:52.918 --> 00:36:02.278
Um, now you can also start asking questions that.

366
00:36:02.278 --> 00:36:07.079
Um.

367
00:36:10.559 --> 00:36:14.338
Let's say that, um.

368
00:36:14.338 --> 00:36:18.958
Hello.

369
00:36:20.278 --> 00:36:26.489
He's still alive.

370
00:36:26.489 --> 00:36:31.259
Say at a time.

371
00:36:31.259 --> 00:36:36.028
5, okay. What's the probability?

372
00:36:37.378 --> 00:36:41.668
It's a high quality.

373
00:36:41.668 --> 00:36:45.478
The quality of heart.

374
00:36:45.478 --> 00:36:49.498
Well, I'll work you through Parkway to get the idea. This is.

375
00:36:49.498 --> 00:36:52.889
Um.

376
00:36:52.889 --> 00:36:56.398
So, good well.

377
00:37:00.239 --> 00:37:09.418
Cool.

378
00:37:09.418 --> 00:37:16.469
Could we do that um.

379
00:37:16.469 --> 00:37:23.699
Again, so the probability that this is the probability that, um.

380
00:37:25.768 --> 00:37:31.438
That it dies that time K and that the probability of a given high.

381
00:37:31.438 --> 00:37:37.378
Hi, what's the problem with K given low.

382
00:37:37.378 --> 00:37:41.668
The problem is is low, which is, um.

383
00:37:43.199 --> 00:37:48.179
Are 1-R to the K and it's 1 time.

384
00:37:48.179 --> 00:37:53.159
Time on mine attached to the K -1 time.

385
00:37:53.159 --> 00:37:57.838
Minus alpha. Okay so.

386
00:37:59.608 --> 00:38:02.608
Hey.

387
00:38:02.608 --> 00:38:07.829
And you've got the components, obviously the probability of K.

388
00:38:07.829 --> 00:38:12.030
And Hi, is the probability of the case.

389
00:38:12.030 --> 00:38:19.019
Hi, there hi. Is that 1st thing there are 1-R to the.

390
00:38:19.019 --> 00:38:23.550
A -1 time a lot.

391
00:38:23.550 --> 00:38:30.119
Okay, you got to recognize some of it.

392
00:38:32.670 --> 00:38:36.329
Hello.

393
00:38:38.579 --> 00:38:43.949
Hello.

394
00:38:49.170 --> 00:38:56.099
And now we start going backwards. The probability that is.

395
00:38:56.099 --> 00:39:06.269
That we're aligned with that probably we die in time K and it's high. It's also the probability that it's high.

396
00:39:06.269 --> 00:39:10.230
And we're aligned with K.

397
00:39:10.230 --> 00:39:13.320
Given a live okay. Time to call the.

398
00:39:13.320 --> 00:39:17.579
Okay, so.

399
00:39:17.579 --> 00:39:20.909
So, probably high given that.

400
00:39:20.909 --> 00:39:25.530
Well, we 1st, exactly. Okay. Is that we exactly die time Kay?

401
00:39:25.530 --> 00:39:30.900
This is the probability of Kay and high divided by the profitability.

402
00:39:30.900 --> 00:39:35.070
Okay, there.

403
00:39:36.780 --> 00:39:44.039
Okay, and pie was, um.

404
00:40:00.625 --> 00:40:01.255
Uh.

405
00:40:06.869 --> 00:40:11.880
The 2nd.

406
00:40:14.159 --> 00:40:17.610
Hello.

407
00:40:17.610 --> 00:40:21.210
Hello hi.

408
00:40:21.210 --> 00:40:26.699
Bye.

409
00:40:30.239 --> 00:40:34.679
Okay, so.

410
00:40:36.960 --> 00:40:42.030
That would be like the probability if I've done it. Right? The probability that the high quality part.

411
00:40:42.030 --> 00:40:45.960
If it dies at time. Okay.

412
00:40:48.630 --> 00:40:54.210
So, in words that the probability.

413
00:40:54.210 --> 00:40:59.909
Hello.

414
00:41:01.079 --> 00:41:08.699
Hello.

415
00:41:08.699 --> 00:41:14.519
And this could get more and K gets bigger.

416
00:41:17.070 --> 00:41:21.300
Is there.

417
00:41:21.300 --> 00:41:28.199
Larger the function 1 factor protein.

418
00:41:28.199 --> 00:41:31.289
That's a little Holy parts to die.

419
00:41:31.289 --> 00:41:35.219
That's how we can start doing your life and stuff like that.

420
00:41:35.219 --> 00:41:41.969
Um.

421
00:41:43.079 --> 00:41:47.730
Want to switch to doing another, for example.

422
00:41:47.730 --> 00:41:52.739
So.

423
00:41:52.739 --> 00:41:56.789
Hey.

424
00:41:59.550 --> 00:42:05.369
Okay.

425
00:42:07.800 --> 00:42:12.929
So, again, um, so.

426
00:42:14.880 --> 00:42:17.940
Okay.

427
00:42:19.590 --> 00:42:26.909
Hmm.

428
00:42:33.329 --> 00:42:38.639
And the expected value alpha.

429
00:42:38.639 --> 00:42:43.019
And probably okay is a probability.

430
00:42:44.670 --> 00:42:49.889
Hey, that's happening.

431
00:42:51.119 --> 00:42:57.539
Happening and whatever, um.

432
00:42:57.539 --> 00:43:01.500
I know so 1.

433
00:43:01.500 --> 00:43:05.940
I don't know, let's do 1 minute. Let's say whatever.

434
00:43:09.840 --> 00:43:12.900
Is the average number.

435
00:43:17.610 --> 00:43:23.250
Been an hour doesn't matter. Okay. So, um.

436
00:43:23.250 --> 00:43:27.659
Let's give an example, um.

437
00:43:27.659 --> 00:43:32.730
Huh.

438
00:43:33.900 --> 00:43:39.210
Calls to a call center.

439
00:43:41.489 --> 00:43:45.269
And let's say, um.

440
00:43:45.269 --> 00:43:49.019
Okay.

441
00:43:50.460 --> 00:43:56.369
They can per minute so this is.

442
00:43:58.230 --> 00:44:06.900
That's the potential callers are independent.

443
00:44:10.289 --> 00:44:17.039
Okay, and so let's say, maybe, let's say.

444
00:44:17.039 --> 00:44:20.699
There is any equal, say, 300.

445
00:44:22.710 --> 00:44:27.239
Possible color.

446
00:44:28.920 --> 00:44:35.579
And property of any.

447
00:44:35.579 --> 00:44:43.139
Specific 1 calling following in the next minute.

448
00:44:48.900 --> 00:44:53.550
Is.

449
00:44:55.619 --> 00:45:00.480
Over 30Million so the expected number.

450
00:45:03.090 --> 00:45:06.960
N, P12 to 10.

451
00:45:08.639 --> 00:45:12.030
And.

452
00:45:12.030 --> 00:45:19.710
So now, in the real world, you're smart people here, you're an RPI you'll figure out the math, you'll figure out the equation.

453
00:45:19.710 --> 00:45:28.230
And once you do that, the remaining hard part is, are the equations, the proper 1 to use.

454
00:45:28.230 --> 00:45:32.369
The hard questions are, are your assumptions accurate?

455
00:45:32.369 --> 00:45:36.269
And something like call centers, this assumes that.

456
00:45:36.269 --> 00:45:39.329
Of the 300Million people who might call, but.

457
00:45:39.329 --> 00:45:43.920
There's no common call is going to make a call at what okay.

458
00:45:45.449 --> 00:45:52.079
So, you know, maybe there's some popular TV show, and they're going to call during ads. So they're correlated.

459
00:45:52.079 --> 00:45:57.179
Except if it's a Super Bowl, they're going to call during the game and watch the ads. Maybe. So.

460
00:45:57.179 --> 00:46:06.599
So, in that case, the potential colors are correlated in that case, this math doesn't work. But if.

461
00:46:06.599 --> 00:46:14.369
All 300Million possible callers. Each of them has a 130Million probability calling the next minute. Then this works out.

462
00:46:15.510 --> 00:46:20.909
But any case, so, alpha here would be 10.

463
00:46:20.909 --> 00:46:24.840
For a minute.

464
00:46:27.539 --> 00:46:31.619
So.

465
00:46:33.269 --> 00:46:37.559
The probability of exactly.

466
00:46:37.559 --> 00:46:40.949
1 call this minute.

467
00:46:43.079 --> 00:46:47.280
Is, um.

468
00:46:47.280 --> 00:46:51.690
For the 1 on 1 factory to the minus alpha. So that's.

469
00:46:51.690 --> 00:46:55.469
10 times 8 of the -10.

470
00:46:56.940 --> 00:47:01.769
We're going to nasty feeling. We did something wrong. My mind is Louis. Um.

471
00:47:07.710 --> 00:47:11.699
Mm, hmm.

472
00:47:11.699 --> 00:47:17.159
Hello.

473
00:47:17.159 --> 00:47:22.710
So, whatever, um.

474
00:47:22.710 --> 00:47:28.440
Now, I could say, um.

475
00:47:28.440 --> 00:47:33.179
Probability of 10 call.

476
00:47:34.320 --> 00:47:39.150
Wouldn't be end of the 10th over 10 factorial.

477
00:47:39.150 --> 00:47:42.480
Okay.

478
00:47:43.559 --> 00:47:46.920
No, um, okay.

479
00:47:46.920 --> 00:47:55.409
That's in a minute. In a minute, I suppose I want the probability in an hour.

480
00:47:55.409 --> 00:48:01.469
So.

481
00:48:06.510 --> 00:48:13.739
The probability.

482
00:48:15.179 --> 00:48:18.840
For an hour long interval interval. Okay. Okay.

483
00:48:18.840 --> 00:48:28.289
Well, then things to scale up linearly. So, um.

484
00:48:31.739 --> 00:48:35.039
So the expected, it doesn't mean here.

485
00:48:36.119 --> 00:48:42.630
Meaning for the hour, it was 60 times the mean for the minute.

486
00:48:44.460 --> 00:48:51.690
It goes up later, like the call, this 1 beta let's say it'll be 60 so.

487
00:48:51.690 --> 00:48:59.250
Equals 10 of the data will be 600 so on. So, um.

488
00:49:02.250 --> 00:49:05.579
Probability of let's say.

489
00:49:05.579 --> 00:49:10.409
1000 calls in an hour.

490
00:49:12.150 --> 00:49:15.480
Call that thing, Kay, or something. We'll be.

491
00:49:16.619 --> 00:49:23.489
Related to the K over K Victoria the beta, which is.

492
00:49:25.829 --> 00:49:30.000
Of 600.

493
00:49:35.820 --> 00:49:43.889
And so on, so you can start using.

494
00:49:45.269 --> 00:49:54.869
Start here and then the probability is this less than 5 calls and solving some of the cases for.

495
00:49:54.869 --> 00:49:57.900
Um.

496
00:49:57.900 --> 00:50:05.099
Okay, so that we can play games or something like that.

497
00:50:07.199 --> 00:50:12.630
So, I've given you the main points in.

498
00:50:14.760 --> 00:50:19.230
In chapter 3, I'll review a few things more on Thursday, but that's.

499
00:50:19.230 --> 00:50:24.659
I've given you all the highlights, so on at all, put up another homework real soon.

500
00:50:24.659 --> 00:50:29.099
Now, chapter.

501
00:50:29.099 --> 00:50:34.650
Okay, the next chapter, or I guess is.

502
00:50:34.650 --> 00:50:38.789
Introduces some new ideas.

503
00:50:38.789 --> 00:50:43.289
And.

504
00:50:43.289 --> 00:50:46.349
So.

505
00:50:46.349 --> 00:50:49.650
Sure.

506
00:50:49.650 --> 00:50:58.829
New ideas in chapter 4 is something called a cumulative distribution function and I'll define it and give examples.

507
00:51:02.429 --> 00:51:06.510
The kid the point of the human distribution function.

508
00:51:06.510 --> 00:51:10.800
Is it the idea that works with the screen that was continuous?

509
00:51:12.599 --> 00:51:17.250
You know, anyone else.

510
00:51:19.110 --> 00:51:23.340
Okay, so.

511
00:51:25.590 --> 00:51:30.329
Chapter 4.

512
00:51:30.329 --> 00:51:34.019
Sneaky.

513
00:51:35.460 --> 00:51:43.769
Okay.

514
00:51:45.869 --> 00:51:51.000
Um, and.

515
00:51:51.000 --> 00:51:54.900
It's on the notation.

516
00:51:54.900 --> 00:52:00.960
It's not for case letters.

517
00:52:03.480 --> 00:52:07.079
Like.

518
00:52:08.460 --> 00:52:13.170
Okay.

519
00:52:13.170 --> 00:52:17.699
Yeah, that sort of thing.

520
00:52:17.699 --> 00:52:23.340
And, um.

521
00:52:23.340 --> 00:52:30.659
For random variable call it a, or something.

522
00:52:36.480 --> 00:52:40.980
Um.

523
00:52:40.980 --> 00:52:44.730
It's a little.

524
00:52:46.650 --> 00:52:50.489
Hmm.

525
00:52:53.969 --> 00:52:57.300
But, okay.

526
00:52:57.300 --> 00:53:02.369
Okay.

527
00:53:02.369 --> 00:53:07.409
Or you could also write it with something like.

528
00:53:07.914 --> 00:53:22.315
Access might be better. So it's the probability that the random variable is less than, or equal.

529
00:53:22.619 --> 00:53:27.480
To that thing, and the last the equal matters. Let me give you an example.

530
00:53:27.480 --> 00:53:35.460
Um, fair coin.

531
00:53:36.780 --> 00:53:42.300
I got to go and buy some biased coins just to light in the class off or something. Um.

532
00:53:43.380 --> 00:53:48.929
Right. I like the word price, but not many people know what it means.

533
00:53:48.929 --> 00:53:57.630
Um, mobility is 0, heads is 4th, 1 head is.

534
00:53:57.630 --> 00:54:03.030
8 create probably a 2 heads of create.

535
00:54:03.030 --> 00:54:06.599
Although the 3 had the.

536
00:54:07.889 --> 00:54:13.050
I can forward it. Okay. Um, 1, 8 create.

537
00:54:16.679 --> 00:54:20.250
So this is K here 0, 1, 2, 3.

538
00:54:20.250 --> 00:54:23.489
And this, here's 1, 8, 3.

539
00:54:24.780 --> 00:54:28.289
This is K. probably. Okay. Okay.

540
00:54:28.289 --> 00:54:33.809
Okay, that the.

541
00:54:33.809 --> 00:54:39.119
Okay, now the CDF looks like this, um.

542
00:54:41.250 --> 00:54:45.480
I'll draw this together next page.

543
00:54:45.480 --> 00:54:51.599
So, we got colors here, so.

544
00:54:53.070 --> 00:54:56.340
1, 8.

545
00:54:56.340 --> 00:54:59.340
Are you doing.

546
00:54:59.340 --> 00:55:04.230
For the meeting, so.

547
00:55:04.230 --> 00:55:09.989
The, I'll do in blue.

548
00:55:11.039 --> 00:55:18.869
So that's okay. That's the human distribution starts off like this.

549
00:55:18.869 --> 00:55:23.550
Starts off 0, jumps up to date.

550
00:55:25.139 --> 00:55:31.800
Up the 48 it jumps up to 7 and 8.

551
00:55:31.800 --> 00:55:35.070
Okay.

552
00:55:36.090 --> 00:55:41.460
So so this is the level here's 108, global 4 8.

553
00:55:41.460 --> 00:55:44.789
Oh, 7, 8, 1.

554
00:55:44.789 --> 00:55:49.650
So this is the org.

555
00:55:49.650 --> 00:55:57.179
So, now we can use this graph to ask.

556
00:56:00.269 --> 00:56:03.510
What's the problem of the number of heads.

557
00:56:05.730 --> 00:56:11.639
It's less than or equal to 1.8. okay.

558
00:56:11.639 --> 00:56:17.130
So, we go and look at 1.8 here and the answer is, um.

559
00:56:19.679 --> 00:56:24.780
Equals equal 1 half. Okay. Let me put it in.

560
00:56:27.869 --> 00:56:30.900
What's the probability number of head?

561
00:56:32.849 --> 00:56:38.699
Is between, I don't know.

562
00:56:38.699 --> 00:56:41.880
2 thirds and 5.

563
00:56:41.880 --> 00:56:45.900
Now, we have by minus f of 2 thirds.

564
00:56:45.900 --> 00:56:49.230
Equals 1-1 a.

565
00:56:50.369 --> 00:57:00.389
70, so, even if our random variable is all the interviews or something like number of heads.

566
00:57:00.389 --> 00:57:08.760
This CDF is cumulative function is defined for fraction falls over any real number for -1 phase of plus affinity.

567
00:57:08.760 --> 00:57:13.139
And so the vertical red line here are, um.

568
00:57:14.219 --> 00:57:23.460
The callers can we get here?

569
00:57:25.409 --> 00:57:29.940
The vertical red line, something like that.

570
00:57:33.269 --> 00:57:38.369
But what the CDF does is something like this.

571
00:57:46.139 --> 00:57:50.579
Okay, so.

572
00:57:50.579 --> 00:57:58.710
New idea, so it's a step function, takes a jump up whatever it is a non 0 probability of.

573
00:57:58.710 --> 00:58:02.969
But I do value yes, yes.

574
00:58:02.969 --> 00:58:06.329
Hello.

575
00:58:06.329 --> 00:58:13.860
2.3 become 1 because the, for 5 equals 1.

576
00:58:13.860 --> 00:58:19.320
It's going to be we're here at 5.

577
00:58:20.849 --> 00:58:24.030
Take a darker color, um.

578
00:58:24.030 --> 00:58:32.309
Orange and the CDF at 2 thirds is over here.

579
00:58:32.309 --> 00:58:38.699
So, we generalize the concept so it's defined for anything from minus that.

580
00:58:38.699 --> 00:58:44.099
So, the probability we got less than or equal to a 1Million heads is 1.

581
00:58:44.099 --> 00:58:47.969
The probably only be done last or equal to -3. 0.

582
00:58:47.969 --> 00:58:54.210
So, it's defined, it starts at 0. it's always monitoring monitor.

583
00:58:54.210 --> 00:59:00.690
Hello.

584
00:59:00.690 --> 00:59:05.610
Okay.

585
00:59:05.610 --> 00:59:11.909
Reason for this definition is, I'm setting you up to handle continuous rapid variables.

586
00:59:11.909 --> 00:59:15.179
On Thursday.

587
00:59:21.360 --> 00:59:25.650
Give you another question.

588
00:59:25.650 --> 00:59:32.880
Okay, let's do a uniform writing variable.

589
00:59:34.980 --> 00:59:38.610
Yeah, I see let me start the next page papers. 2.

590
00:59:38.610 --> 00:59:43.380
Um.

591
00:59:43.380 --> 00:59:48.599
Okay.

592
00:59:48.599 --> 00:59:52.409
And so let's say.

593
00:59:52.409 --> 00:59:58.349
It's from 0 to 4, let's say.

594
00:59:59.760 --> 01:00:07.619
Okay, so the probability is 0, it was a 51 dollar value equals probability of for.

595
01:00:07.619 --> 01:00:12.030
It was 1. okay so if I for it.

596
01:00:12.030 --> 01:00:19.920
It's a, it's like.

597
01:00:22.530 --> 01:00:26.670
1, 2, 3, 4.

598
01:00:27.869 --> 01:00:31.590
That's the probability. So okay.

599
01:00:31.590 --> 01:00:39.300
For the big okay.

600
01:00:39.300 --> 01:00:42.780
It will start off as 0 and will jump to a fish.

601
01:00:42.780 --> 01:00:46.590
We'll jump to 7th jumps to 3.

602
01:00:46.590 --> 01:00:50.280
The 4 to 5.

603
01:00:50.280 --> 01:00:53.909
So, this.

604
01:00:53.909 --> 01:00:57.360
Here is 105.

605
01:00:57.360 --> 01:01:00.360
451.

606
01:01:01.469 --> 01:01:08.849
So, what it looks like removing all the other stuff is bang.

607
01:01:15.389 --> 01:01:21.239
Goes out here, in my opinion, cause I take care of.

608
01:01:21.239 --> 01:01:27.750
And it jumps up at the probability so.

609
01:01:27.750 --> 01:01:30.869
So here the probability.

610
01:01:30.869 --> 01:01:33.960
Not the number of pages less than or equal to.

611
01:01:33.960 --> 01:01:38.519
3.14 look in here.

612
01:01:38.519 --> 01:01:45.780
And it's equal to build a number of heads is less than equal to 20.

613
01:01:45.780 --> 01:01:52.139
Equals 1, I'll build a number of pages last year with the .

614
01:01:52.139 --> 01:01:55.170
5, 0.

615
01:01:55.170 --> 01:02:01.889
Yes.

616
01:02:01.889 --> 01:02:07.050
So, we find the capital 1.

617
01:02:07.050 --> 01:02:13.380
Adding the, probably up to 34 up to and including.

618
01:02:13.380 --> 01:02:17.820
That's important for these things that take job. So.

619
01:02:19.110 --> 01:02:22.920
Okay.

620
01:02:22.920 --> 01:02:27.900
So, I'm working out the work, it might be a fraction or something like, for.

621
01:02:27.900 --> 01:02:32.309
All right.

622
01:02:34.349 --> 01:02:37.380
And we can do intervals so.

623
01:02:37.380 --> 01:02:41.340
So.

624
01:02:42.449 --> 01:02:46.559
The probability that.

625
01:02:46.559 --> 01:02:51.750
3.14.

626
01:02:51.750 --> 01:02:57.119
Listen K, less than or equal to 20.

627
01:02:57.119 --> 01:03:00.630
It was 1-point 84.2 and so on.

628
01:03:02.099 --> 01:03:06.389
Like that okay.

629
01:03:06.389 --> 01:03:10.139
Okay.

630
01:03:19.769 --> 01:03:22.949
Again, that's what the call the team.

631
01:03:38.130 --> 01:03:42.269
Hello.

632
01:03:49.679 --> 01:03:54.389
Thing.

633
01:03:54.389 --> 01:04:01.349
And is not always a good formula for it and it may not always, it doesn't always simplify.

634
01:04:03.630 --> 01:04:11.250
That could be a reasonable point to stop by saying that's the natural stopping point. Um.

635
01:04:12.630 --> 01:04:20.309
So, what I showed you today, just to review is 1st, I worked out some various things.

636
01:04:20.309 --> 01:04:26.219
The variance for a binomial function.

637
01:04:26.219 --> 01:04:32.400
Start a new guards for geometric function and showing you some techniques you can use to calculate things like that. So.

638
01:04:32.400 --> 01:04:40.980
A good expression on derivatives of it and showed some conditional things. Like, if we had the part.

639
01:04:40.980 --> 01:04:47.039
The factories making high quality and low quality parts there's 2 machines that are put together.

640
01:04:47.039 --> 01:04:50.909
So, we could find we can do.

641
01:04:50.909 --> 01:04:54.599
It's like, are you based function as phase will actually.

642
01:04:54.599 --> 01:05:01.949
And we can find the mean apart when we didn't know which it was good or bad.

643
01:05:01.949 --> 01:05:05.400
But we had the probability that it was good. That was the alpha then we could.

644
01:05:05.400 --> 01:05:12.239
Find the mean, if we don't know what the part is, take the conditional means, wait it by the probability that it's good or bad.

645
01:05:12.239 --> 01:05:17.820
And to a variance of the whole thing, when we don't know.

646
01:05:17.820 --> 01:05:24.150
We work with the partner for veterans, which involves the expectation of X squared minus required.

647
01:05:24.150 --> 01:05:29.760
And again, it's a total probability things a conditional on. It'd be good. I'd probably good to go on.

648
01:05:29.760 --> 01:05:35.699
So, we saw stuff like that some more examples of the, um.

649
01:05:35.699 --> 01:05:41.579
Brandon variable that call centers and saw.

650
01:05:41.579 --> 01:05:44.760
And the thing scales up, obviously if it's.

651
01:05:44.760 --> 01:05:50.730
A, it's a number of colors in a minute is a cost on with sub mean alpha.

652
01:05:50.730 --> 01:05:55.949
And the number of colors in an hour will also be plus on with the meaning of 60, alpha.

653
01:05:55.949 --> 01:05:59.579
It scales like that nicely.

654
01:05:59.579 --> 01:06:06.510
So, and then I introduce you to stop the 1st item from the chapter.

655
01:06:06.510 --> 01:06:15.750
Kill the distribution function, and the reason it's got that weird definition where a fracture is a legal argument.

656
01:06:15.750 --> 01:06:19.559
Is the next thing we're going to see is a.

657
01:06:19.559 --> 01:06:25.199
Probability distribution for continuous, random variables for the random variables. The real number.

658
01:06:27.385 --> 01:06:41.155
That's enough stuff for today, I'll stay in the middle of his questions. Other than that. I hope the recording works this time next the following me out on the problem with that and I'll say this stuff is uploaded.

659
01:06:42.355 --> 01:06:42.534
So.

660
01:06:43.110 --> 01:06:46.260
Right.

661
01:06:46.260 --> 01:06:49.889
Hello.

662
01:06:49.889 --> 01:06:57.539
Sure.

663
01:07:00.900 --> 01:07:06.329
We have to learn.

664
01:07:06.329 --> 01:07:10.050
On your your Monday.

665
01:07:10.050 --> 01:07:24.420
Well, that's 1 geometric is the number of costs for some other things like great.

666
01:07:24.420 --> 01:07:27.869
Those are the things. Yeah and I.

667
01:07:27.869 --> 01:07:37.679
Mother's day.

668
01:07:37.679 --> 01:07:41.969
You want to scroll back from here.

669
01:07:46.230 --> 01:07:51.090
You want to pay back and forth.

670
01:07:59.130 --> 01:08:03.269
Hm.

671
01:08:03.269 --> 01:08:07.409
Hello.

672
01:08:07.409 --> 01:08:10.650
Hello.

673
01:08:14.190 --> 01:08:17.550
Yeah.

674
01:08:17.550 --> 01:08:21.029
Hello.

675
01:08:21.029 --> 01:08:26.850
Email me. Okay.

676
01:08:26.850 --> 01:08:32.100
I'll give you more time.

677
01:08:32.100 --> 01:08:36.869
Funny.

678
01:08:36.869 --> 01:08:41.369
But.

679
01:08:41.369 --> 01:08:50.729
File the file and the field thing in greater scope and say there's a problem with the textbook and also say that.

680
01:08:50.729 --> 01:08:55.680
Hello.

681
01:08:55.680 --> 01:09:01.199
Yeah, I put something so you got part points taken off and homework. 1.

682
01:09:01.199 --> 01:09:08.069
Yeah, yeah, so there's a thing that integrated scope you can file for recreate it and say that I told them.

683
01:09:08.069 --> 01:09:12.239
And I was.

684
01:09:12.239 --> 01:09:18.300
Yeah, but submitted the great result when great scopes open, but don't but then you can do.

685
01:09:18.300 --> 01:09:22.680
I know to.

686
01:09:22.680 --> 01:09:31.859
Where is it is on your workspace? I was supposed to be upgraded. There's been some great stuff problems, this semester and stories out there, but.

687
01:09:31.859 --> 01:09:35.189
Whenever we get it working, you have a week.

688
01:09:35.189 --> 01:09:42.060
And the mission yeah, so whenever we do within a week, and then I'll be putting a homework for, you.

689
01:09:42.085 --> 01:09:55.765
All right yeah, there's been some more political. I think it's listed in greater scope, but it's listed read out in grade school, right? Okay.

690
01:10:07.614 --> 01:10:12.654
Well, no, an easy expected value that's the average and he is a probability.

691
01:10:13.319 --> 01:10:18.720
So the average value, okay, if we know what the crap part is.

692
01:10:18.720 --> 01:10:23.220
Times the probability of the credit card from the music flow holiday.

693
01:10:24.630 --> 01:10:32.069
Plus the total average is the average. Okay we know what the high quality part type of probability is.

694
01:10:32.069 --> 01:10:39.090
Plus the average expected value. Okay if we know the low part of the probability is.

695
01:10:40.710 --> 01:10:44.970
Confused because of.

696
01:10:44.970 --> 01:10:49.050
Hello.

697
01:10:49.050 --> 01:10:52.800
I could.

698
01:10:52.800 --> 01:11:02.130
How would you find the this is kind of thing well, this 1 here I put up here the probability.

699
01:11:02.130 --> 01:11:09.119
Here, if it's a high quality part probability that it's exactly a time case.

700
01:11:09.119 --> 01:11:13.619
At the local at that point there.

701
01:11:14.640 --> 01:11:17.640
And the probability high quality card is.

702
01:11:17.640 --> 01:11:26.579
The probability is it? Yes, if it's and then how would you calculate that?

703
01:11:26.579 --> 01:11:31.829
Okay, well that we take the 2 of these.

704
01:11:31.829 --> 01:11:35.850
Hello.

705
01:11:37.500 --> 01:11:40.680
Hello.

706
01:11:40.680 --> 01:11:44.850
Okay, see you Thursday.

707
01:11:44.850 --> 01:11:48.539
Hello.

708
01:11:48.539 --> 01:11:53.789
No.

709
01:11:53.789 --> 01:11:58.920
It's you wait the 2 of them, so.

710
01:11:58.920 --> 01:12:06.479
So, this, this actually is the probability it can give him. Oh, this is your idea.

711
01:12:07.649 --> 01:12:13.920
Let me write that down.

712
01:12:13.920 --> 01:12:17.609
So this is the probability.

713
01:12:17.609 --> 01:12:31.470
We already have this is the probability and probability of plan. No was already given up. Yeah. Yeah.

714
01:12:31.470 --> 01:12:34.590
Hello.

715
01:12:34.590 --> 01:12:34.710
Huh.

716
01:13:09.300 --> 01:13:20.340
So so how do your other classes handle, live and remote at the same time?

717
01:13:20.340 --> 01:13:24.923
Mm, hmm.