M 362K, Spring 03, Smith

## Assignment for Monday, October 27

I. Read Section 4.8.1 (p. 158 - 159)

- Why do you think a geometric random variable is
called "geometric"? [Hint: Think of the values of the pmf as a sequence.]

II. Do the following practice problems:

1. p. 178 #66

2. Supose you have a batch of old light bulbs. The probability
that a bulb randomly chosen from this batch is defective is 9/10. You randomly
take a bulb from the batch, screw it into a light socket, and see if the
bulb works. If it does, you stop. If not, you repeat the process until you
find one that does work.

a. What is the probability that you
need to try n bulbs to get one that works?

b. What is the probability that you
need to try at least n bulbs to get one that works?

c. On average, how many bulbs would
someone doing this process expect to try before getting one that works?

3. p. 180 #9

III. Read pp. 199 - 204

IV. Do the practice problem #15 on p. 229.