Cumulative Review, sample questions covering chapters 7 and 8

Random variable X has a mean of 8 and a standard deviation of 4. Random variable Y has a mean of 5 and a standard deviation of 2. Let W = X - 2Y. Assuming that X and Y are independent, calculate the mean and standard deviation of W.

The mean temperature in September was 20 degrees Celsius with a standard deviation of 4.5 degrees. What was the mean and standard deviation of the temperature in Farenheit? (Farenheit = 9/5 Celsius + 32)

The Redskins have 6 games left. Assume that the games are independent and that the Redskins have a 60 percent chance of winning each game.

- What is the probability that they will win exactly 4 out of the 6 remaining games?
- What is the probability that they will win 4 or more games?
- Let Y be the number of games that they win out of the next 6 games. What is the expected value of Y? What is the standard deviation of Y?
- What is the probability that they will win the next three in a row?
- Let X be the number of consecutive wins the Redskins have, starting with the next game (if they lose the next game, X=0). What is the expected value of X?

Which of the following is a valid probability density function when defined over the domain 0<=X<=2?

f(x) = .5x

f(x) = x-1

f(x) = x-
Suppose that we have a roulette wheel with 2 green slots (zero and double-zero), 18 red slots, and 18 black slots. If you bet $1 on red and win, you are plus $1. If you bet $1 on red and lose, you are minus $1. What is the expected value of a $1 bet on red? What is the expected value of a $5 bet on red? What is the standard deviation of a $5 bet on red?

- There are three Presidential primaries on one day. Each state is winner-take all. California has 420 delegates, West Virginia has 120 delegates, and Illinois has 220 delegates. Candidate Smith has a probability of .35 of winning California, .60 of winning West Virginia, and .51 of winning Illinois. What is the expected number of delegates that candidate Smith will win that day?