Expected Value X is a random variable over [1,2] 1. Find distribution function of Y=e$^x$ 2. Find E[Y] i.e expected value of Y I'm done with part a. The answer is 1/y . Can anyone help calculate the expected value. 
The answer to part a is not $\dfrac 1 y$ It is $f_Y(y) = \begin{cases}0 & y < e \\ \dfrac 1 y &y \in [e,e^2] \\ 0 &e^2 < y \end{cases}$ There is a serious difference. $E[Y] = \displaystyle \int_e^{e^2}~y\dfrac 1 y~dy = \int_e^{e^2}~1=e^2e$ 
Romsek is assuming you meant "x is uniformly distributed over [1, 2]". Just saying "x is a random variable over [1, 2]" does not tell us the probability distribution which is necessary in order to answer this question. 
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