Problems in Probability

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Fall 2011 Strategic Practice 9: Section 1 (Beta and Gamma Distributions) - Question 3
Fred waits X ~ Gamma(a, ) minutes for the bus to work, and then waits Y ~ Gamma(b, ) for the bus going home, with X and Y independent. Is the ratio X/Y independent of the total wait time X + Y ?
Solution: As shown in the bank-post office story, W = X / X+Y is independent of X + Y. So any function of W is independent of any function of X + Y. And we have that X/Y is a function of W as X/Y = W / 1-W.
"Mathematics is the logic of certainty, but statistics is the logic of uncertainty."
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