[Solution] Let U be uniform [ 0,1 ] and let X=-(1)/(lambda)ln (1-U). Find the density of the random variable X (since 1-e^-λ y>0). This means that

Question: Let U be uniform $\left[ 0,1 \right]$ and let $X=-\frac{1}{\lambda }\ln \left( 1-U \right)$.

Find the density of the random variable X
(since $1-{{e}^{-\lambda y}}>0$ ). This means that the density is
\[{{f}_{X}}\left( y \right)=\frac{d}{dy}\left( 1-{{e}^{-\lambda y}} \right)=\lambda {{e}^{-\lambda y}}\]
Identify the distribution of X .

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[Solution] Let U be uniform [ 0,1 ] and let X=-(1)/(lambda)ln (1-U). Find the density of the random variable X (since 1-e^-λ y>0). This means that

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