Answered: Suppose that the random variables X, Y,…

Suppose that the random variables X, Y, Z have multivariate PDF fXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. Find (a) fXY(x, y), (b) fYZ(y, z), (c) fZ(z)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 1E

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Question

Suppose that the random variables X, Y, Z have multivariate PDF
f_XYZ(x, y, z) = (x + y)e^−zfor 0 < x < 1, 0 < y < 1, and z > 0.

Find (a) f_XY(x, y), (b) f_YZ(y, z), (c) fZ(z)

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