Let (Z) be a (mathrm{N}(0,1)) random variable. a. Prove that the moment generating function of (X) is

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Let $Z$ be a $\mathrm{N}(0,1)$ random variable.

a. Prove that the moment generating function of $X$ is $\exp \left[-\frac{1}{2} t^{2}ight]$.

b. Prove that the characteristic function of $X$ is also $\exp \left[-\frac{1}{2} t^{2}ight]$.

c. Using the moment generating function, derive the first three moments of $X$. Repeat the process using the characteristic function.

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Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

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Question Posted: Mar 15, 2024 02:01 AM

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Let (Z) be a (mathrm{N}(0,1)) random variable. a. Prove that the moment generating function of (X) is

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Introduction To Statistical Limit Theory

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