Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 <1). Let X₁, X₂, X, be a random sample of size n from the population of X. (d) Find the method of moments estimator (mme) of 0. (e) Show how the mle of 0 is related to its mme. Explain if it is always true. (f) Verify if X, is a sufficient statistic for 8 or not. 1 (g) Justify if = is an unbiased estimator for 0.

MATLAB: An Introduction with Applications
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Suppose the random variable, X, follows a geometric distribution with parameter (0<
0 <1). Let X₁, X₂, X, be a random sample of size n from the population of X.
(d) Find the method of moments estimator (mme) of 0.
(e) Show how the mle of 0 is related to its mme. Explain if it is always true.
(f) Verify if
X, is a sufficient statistic for 8 or not.
(g) Justify if = is an unbiased estimator for 6.
Transcribed Image Text:Suppose the random variable, X, follows a geometric distribution with parameter (0< 0 <1). Let X₁, X₂, X, be a random sample of size n from the population of X. (d) Find the method of moments estimator (mme) of 0. (e) Show how the mle of 0 is related to its mme. Explain if it is always true. (f) Verify if X, is a sufficient statistic for 8 or not. (g) Justify if = is an unbiased estimator for 6.
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