# Math Help - Poisson process

1. ## Poisson process

Customers arrive at an ATM at the times of a Poisson process with rate of 10 per hour. Suppose that the amount of money withdrawn on each transaction has a mean of $30 and a standard deviation of$20. Find the mean and standard deviation of the total withdrawals in 8 hours.

2. Let $N=(N_t:t \geq 0)$ be your Poisson process and $X_1,X_2,...$ be i.i.d. withdrawal distributions (mean 30 and var 20).

You are looking for $\sum_{i=1}^{N_8} X_i$.

A hint nice hint is that $\mathbb{E}[\mathbb{E}[X|Y]]=\mathbb{E}[X]$.