# Joint and Marginal Probability Distributions

Person takes bus & subway to work. Bus runs every 20 min (X) & subway every 4 min (Y). Assume timing of the bus and subway are independet and uniform.

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I need to find the joint and marginal distribtions for this problem. Since they are independent I know that f(x,y) = fx(x) * fy(y) but do not understand how to take that and the data given in the problem to find the marginal and joint distribtion . I also have to find the Expected value of X & Y.

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TA : The question is not well-defined. What are X and Y? The waiting time?

X is how often the bus runs 20 (wating time 0 < X < 20)

Y is how often the subway runs 4 (wating time 0 < Y < 4)

#### Solution Summary

Joint and Marginal Probability Distributions are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.