# Question: Let X1 X2 Xn be independent and

Let X1, X2, . . . ,Xn be independent and identically distributed positive random variables. For k ≤ n, find

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A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her expected winnings. Show that X and Y are identically distributed and not necessarily independent, then Cov(X + Y, X − Y) = 0 Let X1, . . . ,Xn be independent and identically distributed random variables. Find E[X1|X1 + · · · + Xn = x] Let X be a normal random variable with parameters μ = 0 and σ2 = 1, and let I, independent of X, be such that P{I = 1} = 1/2 = P{I = 0}. Now define Y by In words, Y is equally likely to equal either X or −X. (a) Are X ...Let X be a nonnegative random variable. Prove that E[X] ≤ (E[X2])1/2 ≤ (E[X3])1/3 ≤ . . .Post your question