Probability 08

Exercise

Suppose that two teams play a series of games that ends when one of them has won games. Suppose that each game played is, independently, won by team with probability . Find the expected number of games that are played when

• (a)
• (b) Also, show in both cases that this number is maximized when

Exercise

A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective. Find the expected number of defective items in the sample.

Exercise

Suppose are discrete random variables over . Then is also a random variable. Show

Exercise

Exercise

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win 1.00. (That is, you lose $1.00.) Calculate

• (a) the expected value of the amount you win;
• (b) the variance of the amount you win.