If the moment-generating function of X is M(t) = {e¹ + find the mean, variance, and pmf of X. 2t

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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If the moment-generating function of \( X \) is

\[ M(t) = \frac{2}{5}e^t + \frac{1}{5}e^{2t} + \frac{2}{5}e^{3t}, \]

find the mean, variance, and pmf of \( X \).
Transcribed Image Text:If the moment-generating function of \( X \) is \[ M(t) = \frac{2}{5}e^t + \frac{1}{5}e^{2t} + \frac{2}{5}e^{3t}, \] find the mean, variance, and pmf of \( X \).
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