The moment generating function can be used to find the mean and variance of the normal distribution.

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a. Use derivatives of MX(t) to verify that E(X) = μ and V(X) = σ².
b. Repeat (a) using R_X(t) = ln[M_X(t)], and compare with part (a) in terms of effort.

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Modern Mathematical Statistics With Applications

ISBN: 9783030551551

3rd Edition

Authors: Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton

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Question Posted: Aug 20, 2023 05:25 AM

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The moment generating function can be used to find the mean and variance of the normal distribution.

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The moment generating function MGF of a random variable X is defined as MXt EetX where t is a real n...View the full answer

Modern Mathematical Statistics With Applications

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