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1. Let X be the number of heads in 4 tosses of a fair coin. (a)...

1. Let X be the number of heads in 4 tosses of a fair coin.

(a) What is the probability distribution of X? Please show how probability is calculated.

(b) What are the mean and variance of X?

(c) Consider a game where you win $5 for every head but lose $3 for every tail that appears in 4 tosses of a fair coin. Let the variable Y denote the winnings from this game. Formulate the probability distribution of Y based on the probability distribution of X.

(d) What is the expected value of Y? Would you like to play this game? If so, why? If not, why not?

Math   Statistics-And-Probability   
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