Engineering Probability Class 11 Tues 2019-02-19

Source

1   Last year's exam 1 online

with and w/o answers. See here.

2   The different counting formulae for selecting k items from n

  1. With replacement; order matters: \(n^k\).
  2. W/o replacement; order matters: \(n(n-1)\cdots(n-k+1) = \frac{n!}{(n-k)!}\).
  3. With replacement; order does not matter: \({{n-1+k} \choose k}\)
  4. W/o replacement; order does not matter: \({n\choose k}=\frac{n!}{k!(n-k)!}\).

3   Review questions

  1. Sampling with replacement with ordering: Each day I eat lunch at either the Union, Mcdonalds, Brueggers, or Sage. How many ways can I eat lunch over 5 days next week?
  2. sampling w/o replacement and w/o order: How many different possible teams of 3 people can you pick from a group of 5?
  3. sampling w/o replacement and with order: 5 people run a race for gold, silver, bronze. How many ways can the medals be won, w/o any ties?
  4. binomial: A coin falls heads with p=.6. You toss it 3 times. What's the probability of 2 heads and 1 tail?
  5. multinomial: You play 38-slot roulette 3 times. Once you got red, once black and once 0 or 00. What was the probability?
  6. conditional probability: You have 2 dice, one 6-sided and one 12-sided. You pick one of them at random and throw it w/o looking; the top is 2. What's the probability that you threw the 6-sided die?
  7. What's the expected number of times you'll have to toss the unknown die to get your first 2?
  8. Independence: Consider {1,2,3,...12}. Is the set of even numbers independent of the set of multiples of 3? What if we use {1,2,..10}?
  9. Useful review questions from the text.
    1. 2.83 on page 90.
    2. 2.99.
    3. 3.5 on page 130.
    4. 3.9.
    5. 3.15.
    6. 3.26.
    7. 3.88 on page 139.

4   Iclicker

  1. We often add a check bit to an 8-bit byte, and set it so there are an odd number of 1 bits. When we read the byte, which is now 9 bits, if there are an even number of 1 s, then we know that there was an error.

    Assume that the probability of any one bit going bad is 1e-10. (The real number is much smaller.)

    What is the probability of the byte going bad (within 1 significant digit)?

    1. 1e-10
    2. 8e-10
    3. 9e-10
    4. 3.6e-19
    5. 7.2e-19

  2. What is the probability of the byte going bad, but we don't notice that (because there were 2 bad bits)?

    1. 1e-10
    2. 8e-10
    3. 9e-10
    4. 3.6e-19
    5. 7.2e-19