B3. Let us consider two discrete uniform distributions X - U({1,2,..., k}) and Y - U({0, k}). Compute the probability generating functions (p.g.f.s) of X and Y. If X and Y are assumed to be...

Extracted text: B3. Let us consider two discrete uniform distributions X - U({1,2,..., k}) and Y - U({0, k}). Compute the probability generating functions (p.g.f.s) of X and Y. If X and Y are assumed to be independent, use these p.g.f.s to obtain the p.g.f. of X + Y. What is then the distribution of X +Y? Hint: You may want to use " 1-zP+1 1-r for x + 1, and that (a+b)(a-b) = a² - b n=0