Let X1, . . . ,Xn be independent exponential random variables having a common parameter λ. Determine the distribution of min(X1, . . . ,Xn).
Answer to relevant QuestionsConsider n independent flips of a coin having probability p of landing on heads. Say that a changeover occurs whenever an outcome differs from the one preceding it. For instance, if n = 5 and the outcome is HHTHT, then there ...Let X have moment generating function M(t), and define ψ(t) = logM(t). Show that ψ′′(t)|t=0 = Var(X) A coin having probability p of landing on heads is flipped n times. Compute the expected number of runs of heads of size 1, of size 2, and of size k, 1 ≤ k ≤ n. For a group of 100 people, compute (a) The expected number of days of the year that are birthdays of exactly 3 people: (b) The expected number of distinct birthdays. If X and Y are independent and identically distributed with mean μ and variance σ2, find E[(X − Y)2]
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