Let be an exponentially distributed random variable with mean . Define a random variable in the following way: if
b) Show that your answer to part a) can be written as:
I would think for a) it would be , but this doesn't seem right since k is not continuous.
and for b) I would think that you have to manipulate the function you got in a) to get what is shown, but am clueless on how to do so. Any help would be greatly appreciated.