# Question

Let X1, X2, X3 denote a random sample of size n = 3 from a distribution with the geometric pmf

(a) Compute P(X1 = 1, X2 = 3, X3 = 1).

(b) Determine P(X1 + X2 + X3 = 5).

(c) If Y equals the maximum of X1, X2, X3, find P(Y ≤ 2) = P(X1 ≤ 2)P(X2 ≤ 2)P(X3 ≤ 2)

(a) Compute P(X1 = 1, X2 = 3, X3 = 1).

(b) Determine P(X1 + X2 + X3 = 5).

(c) If Y equals the maximum of X1, X2, X3, find P(Y ≤ 2) = P(X1 ≤ 2)P(X2 ≤ 2)P(X3 ≤ 2)

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