3. 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?

3. 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?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Question

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

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