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SOLVED: Suppose that X and Y are independent geometric random variables with the same parameter p.What is the probability PX = i|X Y = n? You may find one or both of these formulas, for the sums of a geometric sequence and series, helpful:Σ(tk) = (n 1)tk and Σ(r^k) = 1/(1-r)k=0Explain your result intuitively. Hint: think about how many ways the result you're conditioning on can occur.
SOLVED: Suppose that X and Y are independent geometric random variables with the same parameter p.What is the probability PX = i|X Y = n? You may find one or both of these formulas, for the sums of a geometric sequence and series, helpful:Σ(tk) = (n 1)tk and Σ(r^k) = 1/(1-r)k=0Explain your result intuitively. Hint: think about how many ways the result you're conditioning on can occur.
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