If I am given X that follows an exponential distribution with mean m and Y that follows a poisson distribution with mean n, how can I use them to find the conditional probability density function of X given Y=y? X and Y are dependent.
The waiting time for a customer to be served at a bank follows an exponential distribution with mean 5. On any particular day, the number of customers visiting the bank follows a Poisson distribution with mean 10. Deﬁne the total waiting time S_N = X_1 + X_2 + · · · + X_N where X_i is the waiting time of the ith customer, and N is the number of customers.
This is the question I'm given to find the conditional probability density function of S_N given N=n.