Problem 1 X and Y are independent, identically distributed, binomial discrete random variables. Find the distribution of Z = X + Y. Solution If the range of X and Y is {0, 1, 2, ..., n}, then the range of Z will be {0, 1, 2, ..., 2n}. Z will also have binomial distribution, evaluated by convolving the distributions of X and Y, p? (?) = p ?(?) = ( 2)p ?(1-p) "-? to obtain p? (?) = p ?(?) * p?(?) = ( 2)p?(1-p) 2n