Let (X) be a continuous random variable having probability density function [f(x)= begin{cases}2 e^{-2 x} & text

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Let $X$ be a continuous random variable having probability density function

\[f(x)= \begin{cases}2 e^{-2 x} & \text { for } x>0 \\ 0 & \text { elsewhere }\end{cases}\]

(a) Find the moment generating function.

(b) Obtain $E(X)$ and $E\left(X^{2}\right)$ by differentiating the moment generating function.

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Probability And Statistics For Engineers

ISBN: 9780134435688

9th Global Edition

Authors: Richard Johnson, Irwin Miller, John Freund

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Question Posted: Apr 23, 2024 07:00 AM

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Let (X) be a continuous random variable having probability density function [f(x)= begin{cases}2 e^{-2 x} & text

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Probability And Statistics For Engineers

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