Let be an exponentially distributed random variable with mean . Define a random variable in the following way: if

a)Find

b)Show that your answer to parta)can be written as:

I would think fora)it would be , but this doesn't seem right since k is not continuous.

and forb)I would think that you have to manipulate the function you got ina)to get what is shown, but am clueless on how to do so. Any help would be greatly appreciated.