Let X = (X1, X2,..., Xn) be a sample of i.i.d. Geometric (0) random variables with...

 

Transcribed Image Text:

Let X = (X1, X2,..., Xn) be a sample of i.i.d. Geometric (0) random variables with density function f(x; 0) = 0(1-0), x = 0, 1, 2,...; 0 € (0,1), with mean and variance given by E(X)= 1-0 0 and Var (X) = 1-0 02 Derive the UMVUE of h(0) = 0. Hint: Use the interpretation that P(X₁ = 0) = 0 and the fact that with probability mass function = n i-1 X₁ Negative Binomial (n, 0) Let X = (X1, X2,..., Xn) be a sample of i.i.d. Geometric (0) random variables with density function f(x; 0) = 0(1-0), x = 0, 1, 2,...; 0 € (0,1), with mean and variance given by E(X)= 1-0 0 and Var (X) = 1-0 02 Derive the UMVUE of h(0) = 0. Hint: Use the interpretation that P(X₁ = 0) = 0 and the fact that with probability mass function = n i-1 X₁ Negative Binomial (n, 0)