2. Let X1, X2,..., Xn be independent random variables having the same probability mass function f (x) = e-A" (1 – e^), x = 0, 1, 2, ..., where A is positive. (a) Find the method-of-moment estimator  for A. (b) Find the maximum likelihood estimator A2 for A. (c) Find the efficiency of A1 relative to A2 and the maximum likelihood estimator for P(X1 = 0).

MATLAB: An Introduction with Applications
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2. Let X1, X2,..., Xn be independent random variables having the same probability mass function
f (x) = e-A" (1 – e^), x = 0, 1, 2, ...,
where A is positive.
(a) Find the method-of-moment estimator  for A.
(b) Find the maximum likelihood estimator A2 for A.
(c) Find the efficiency of A1 relative to A2 and the maximum likelihood estimator for P(X1 = 0).
Transcribed Image Text:2. Let X1, X2,..., Xn be independent random variables having the same probability mass function f (x) = e-A" (1 – e^), x = 0, 1, 2, ..., where A is positive. (a) Find the method-of-moment estimator  for A. (b) Find the maximum likelihood estimator A2 for A. (c) Find the efficiency of A1 relative to A2 and the maximum likelihood estimator for P(X1 = 0).
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