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The Exponential pdf for continuous random variable Y takes the form f(y)=\left\{\begin{array}{clc}

\frac{1}{\beta} e^{-y / \beta} & y>0 \\

0 & y \leq 0

\end{array} \quad \text { for } \beta>0\right. Suppose that a new random variable X is defined by

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