Question: 7. Let X1, ..., X,, be a random sample from a geometric distribution, X ~ GEO(p). Find the MLEs of the following quantities: (a) E(X)

7. Let X1, ..., X,, be a random sample from a geometric distribution, X ~ GEO(p). Find the MLEs of the following quantities: (a) E(X) = 1/p. (b) Var(X) = (1 - p)/p?. (c) P[X > k] = (1 - p)* for arbitrary k = 1, 2, ... Hint: Use the invariance property of MLEs. Theorem 9.2.1 Invariance Property If 0 is the MLE of e and if u(0) is a function of 0, then u(0) is an MLE of u(0)

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