Poisson Process: Conditioning and Splitting

Customers arrive at a store as a Poisson process with rate $\lambda = 10$ per hour. Each customer independently buys something with probability $p = 0.3$. (a) What is the distribution of the number of purchases in a 2-hour window? (b) Given that 8 customers arrived in one hour, what is the distribution of the number of purchases? (c) What is the probability that the 3rd purchase happens before time $t = 1$ hour?