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(1) Consider X that follows the Bernoulli distribution with success probability 1/4, that is, P(X =...

(1) Consider X that follows the Bernoulli distribution with success probability 1/4, that is, P(X = 1) = 1/4 and P(X = 0) = 3/4. Find the probability mass function of Y , when Y = X4 . Find the second moment of Y . (2) If X ∼ binomial(10, 1/2), then use the binomial probability table (Table A.1 in the textbook) to find out the following probabilities: P(X = 5), P(2.9 ≤ X ≤ 4.9) (3) A deck of cards contains 10 cards: 6 red cards and 4 black cards. 5 cards are drawn randomly without replacement. What is the probability that exactly 4 red cards are drawn?

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