Question: 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

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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