Each magazine that Charlie reads takes an amount of time that follows an exponential distribution with mean10minutes. The number of magazines that Charlie reads on any given day has a Poisson distribution with mean2. Assume that each reading session always falls within a single day (he does not read past midnight).

Furthermore, suppose that the number of magazines that Charlie reads on different days are independent, and that the lengths of time he takes to read each magazine is also independent of each other.

For simplicity, assume that he only reads 1 magazine at a time and that there are30days in each given month.

Let?be the total number of minutes Charlie spends reading magazines in one month.

Hint:You may find the following useful. For i.i.d. random variables?and a nonnegative random variable?that is independent of all the?'s: