Let X Uniform (0, 1). Suppose that given X = x, Y and Z are independent

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Let X ∼ Uniform (0, 1). Suppose that given X = x, Y and Z are independent and Y |X = x ∼ Uniform(0,x) and Z|X = x ∼ Uniform(0, 2x). Define the random vector U as U = X Y Z

1. Find the PDFs of Y and Z.

2. Find the PDF of U, f_U(u), by using fu(u) = fxyz(x, y, z) = fx(x) fy|x(yx) fz|x,y (z|x,y).

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Related Book For answer-question

Introduction To Probability Statistics And Random Processes

ISBN: 9780990637202

1st Edition

Authors: Hossein Pishro-Nik

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Question Posted: Oct 27, 2023 02:39 AM

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Let X Uniform (0, 1). Suppose that given X = x, Y and Z are independent

Question:

U = X Y Z

Step by Step Answer:

Finding the PDFs of Y and Z Y Since YX x is uniformly distributed on 0 x its probability density fun...View the full answer

Introduction To Probability Statistics And Random Processes

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