Let U Be a Continuous Random Variable with Probability Density $$f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { ( 1 - x ) ^ { 2 } } & 0 \leq x \leq .5 \\0 & \text { else. }\end{array} \right.$$

Short Answer

Let U be a continuous random variable with probability density function $$f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { ( 1 - x ) ^ { 2 } } & 0 \leq x \leq .5 \\0 & \text { else. }\end{array} \right.$$ Using the method of transformations, find the probability density function of $X = e ^ { U + 1 }$ .