Exercise 7.21. Find the distribution of the mixture of Erlang distributions with parameters and geometric distribution with parameter .

Solution:

Exercise 7.22. Find the distribution of the mixture of binomial and Poisson distributions.() ?

Solution:

Exercise 7.23. Let , and independent random variables.

Find the density function of the random sum .

Solution:

By the theorem of total probability

Exercise 7.24. Let be Bernoulli distributed with paramete p and independent random variables.

Find the distribution of .

Solution: