Let the random variables X and Y have a joint PDF which is uniform over the triangle with verticies at (0,0),(0,1), and (1,0). Find the joint PDF of X and Y Find the marginal PDF of Y FInd the condtional PDF of X given Y Find E[X[Y=y], and use the total expectation theorem to find E[X] in terms of E[Y] Use the symmetry of the problem to find the value of E[X]

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let the random variables X and Y have a joint PDF which is uniform over the triangle with verticies at (0,0),(0,1), and (1,0).

Find the joint PDF of X and Y

Find the marginal PDF of Y

FInd the condtional PDF of X given Y

Find E[X[Y=y], and use the total expectation theorem to find E[X] in terms of E[Y]

Use the symmetry of the problem to find the value of E[X]

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