Originally Posted by

**Moo** Hello,

Are you told to let $\displaystyle y_0=\frac b2$ ? because if so, your substitution into the two pdfs is wrong.

You can prove that the integral exists, by taking the limit of the integrand as x tends to 0, and noting that the function is continuous on (0,b). Then in order to solve for the integral, find the power series of $\displaystyle \exp(-bx)$ and hence simplify $\displaystyle \frac 1x (1-\exp(-bx))$

Under certain circumstances (which I suck at stating), you can reverse the integral and the sum signs and it becomes easy to compute.