Engineering Probability Class 13 Thurs 2018-03-01

Source

1   Exam 1 answers

are now online.

We gave full points even if you didn't finish the arithmetic to compute a number. In the real world, you have computers. Also, in the real world, accurate analysis and computation matter. In 1954, physicists made an eensy teensy error designing Castle Bravo.

2   Homework 6

online, due in one week (i.e., Thurs).

3   Notation

How to parse $F_X(x)$

  1. Uppercase F means that this is a cdf. Different letters may indicate different distributions.
  2. The subscript X is the name of the random variable.
  3. The x is an argument, i.e., an input.
  4. $F_X(x)$ returns the probability that the random variable is less or equal to the value x, i.e. prob(X<=x).

4   Matlab

  1. Matlab

    1. Major functions:

      cdf(dist,X,A,...)
pdf(dist,X,A,...)

    2. Common cases of dist (there are many others):

      'Binomial'
'Exponential'
'Poisson'
'Normal'
'Geometric'
'Uniform'
'Discrete Uniform'

    3. Examples:

      pdf('Normal',-2:2,0,1)
cdf('Normal',-2:2,0,1)

p=0.2
n=10
k=0:10
bp=pdf('Binomial',k,n,p)
bar(k,bp)
grid on

bc=cdf('Binomial',k,n,p)
bar(k,bc)
grid on

x=-3:.2:3
np=pdf('Normal',x,0,1)
plot(x,np)

    4. Interactive GUI to explore distributions: disttool

    5. Random numbers:

      rand(3)
rand(1,5)
randn(1,10)
randn(1,10)*100+500
randi(100,4)

    6. Interactive GUI to explore random numbers: randtool

    7. Plotting two things at once:

      x=-3:.2:3
n1=pdf('Normal',x,0,1)
n2=pdf('Normal',x,0,2)
plot(x,n1,n2)
plot(x,n1,x,n2)
plot(x,n1,'--r',x,n2,'.g')

  2. Use Matlab to compute a geometric pdf w/o using the builtin function.

5   Text ctd

  1. Section 4.2.1 page 150.