Suppose that there is a prize ceremony awarding prizes to 10 ?nalists. Each ?nalist is going to get exactly one prize, but assume that each has an equal probability of receiving any given prize. The grand prize is $5000, there are 2 prizes of $2000, 2 prizes of $1000 and 5 prizes of $200. Let X represent the amount of money won by one prize recipient. Find E(X), var(X) and σ for X.
A pair of dice is rolled in a game.
(a) Suppose a success consists of a roll with exactly one of the two dice being 6. Let X denote the number such sucesses. What is the expected value of X if the dice are rolled 10 times?