Referring to Problem 83, show that if the pi are unequal, the sum does not follow a bino...

Referring to Problem 83, show that if the pi are unequal, the sum does not follow a binomial distribution.

Reference

Show that if X_i follows a binomial distribution with n_i trials and probability of success p_i = p, where i = 1, . . . , n and the Xi are independent, then follows a binomial distribution.