Consider a conditional Poisson process in which the rate L is, as in Example 5.29, gamma distributed with parameters m and p. Find the conditional density function of L given that N(t) = n. For the...

Consider a conditional Poisson process in which the rate L is, as in Example 5.29, gamma distributed with parameters m and p. Find the conditional density function of L given that N(t) = n. For the model of Example 5.27, find the mean and variance of the number of customers served in a busy period.