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Q17Section I (Objective (Q1–Q80))17 of 80

Distribution Theory — minimum of geometric random variables

Let (X1,X2,…,Xk)(X_1, X_2, …, X_k) be a random sample of size kk from geometric distribution with parameter pp with pmf f(x)=pqx−1f(x) = pq^{x-1}; x=1,2,3,…x = 1, 2, 3, …. Then min⁡(X1,X2,…,Xk)\min(X_1, X_2, …, X_k) is distributed geometrically with parameter:

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