Questions

What is the best discrete probability distribution in the following cases.

1. (2 points) Your car has five tires (including the spare), which may each independently be flat. The event is that not more than one tire is flat.

   1. Bernoulli
   2. binomial
   3. geometric
   4. Poisson
   5. uniform

2. (2 points) 1,000,000 widgets are made this year, of which 1,000 are bad. You buy 5 at random. The event is that not more than one widget is bad.

   1. Bernoulli
   2. binomial
   3. geometric
   4. Poisson
   5. uniform

3. (2 points) You toss a weighted coin, which lands heads 3/4 of the time.

   1. Bernoulli
   2. binomial
   3. geometric
   4. Poisson
   5. uniform

4. (2 points) You toss a fair 12-sided die.

   1. Bernoulli
   2. binomial
   3. geometric
   4. Poisson
   5. uniform

5. (2 points) You're learning to drive a car, and trying to pass the test. The event of interest is the number of times you have to take the test to pass. Assume that the tests are independent of each other and have equal probability.

   1. Bernoulli
   2. binomial
   3. geometric
   4. Poisson
   5. uniform

6. (2 points) It's Nov 17 and you're outside in a dark place looking for Leonid meteorites. The event of interest is the number of meteorites per hour that you see.

   1. Bernoulli
   2. binomial
   3. geometric
   4. Poisson
   5. uniform

7. (2 points) It's Nov 17.... The new event of interest is the number of seconds until you see the next meteorite.

   1. Bernoulli
   2. binomial
   3. geometric
   4. Poisson
   5. uniform

8. Taxi example: Sometimes there are mixed discrete and continuous r.v.

   1. Let X be the time X to get a taxi at the airport.
   2. 80% of the time a taxi is already there, so p(X=0)=.8.
   3. Otherwise we wait a uniform time from 0 to 20 minutes, so p(a<x<b)=.01(b-a), for 0<a<b<20.

   Questions:

   1. (2 points) For the taxi example, what is F(0)?
      1. 0
      2. .2
      3. .8
      4. .81
      5. 1
   2. (2 points) For the taxi example, what is F(1)?
      1. 0
      2. .8
      3. .81
      4. .9
      5. 1

9. (10 points) Problem 3.50 on page 135 of the text.

10. (15 points) 3.88 on page 139.

11. (15 points) 3.91 (p 139).

Total: 58