If I randomly buy 3 different stocks in a series of orders in a Poisson distributed manner (rate = 50/hr), and I know the probability that I buy stock A, stock B, and stock C, the expected amount of money I spend on each order, and the standard deviation of each order. How would I find the variance for the total amount of money I spend on the stocks over the next hour?
I took the probability of a given stock multiplied by the standard deviation squared, then added each stock A, B, and C, then multiplied the sum by 100. Is that correct?
Use the decomposition of multi-type Poisson processes: for a Poisson process with rate $\lambda$ such that each event in the process is of type $j$ with probability $0\leqslant p_j\leqslant 1$ $($with $\sum_j p_j = 1)$, then the number of type $j$ events are independent Poisson processes with rates $\lambda p_j$.
Do you think you can finish?