Let X1, X2, , Xn be a random sample from a distribution with unknown mean m and variance 2 Show that the method of moments estimators for m and 2 are, respectively, the sample mean and Note that S '2 (n 1) n S '2 where S2 is the sample variance (1 n)E(X X) s i 1

Question: Let X1, X2, . . ., Xn be a random sample from a distribution with unknown mean m and variance 2. Show that the method

Let X1, X2, . . ., Xn be a random sample from a with unknown mean m and variance Ïƒ2. Show that the method of moments estimators for m and Ïƒ2 are, respectively, the sample mean and

Note that S'2 = [(n €“ 1) / n] S'2 where S2 is the sample variance.

= (1/n)E(X -X). s i=1

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