In terms of a positive constant k, random variables X and Y have joint PDF [k+3x² -1/251<1/2, fx,y (x, y) = otherwise. (a) What is k? (b) What is the marginal PDF of X? (c) What is the marginal PDF of Y? (d) Are X and Y independent?

In terms of a positive constant k, random variables X and Y have joint PDF [k+3x² -1/251<1/2, fx,y (x, y) = otherwise. (a) What is k? (b) What is the marginal PDF of X? (c) What is the marginal PDF of Y? (d) Are X and Y independent?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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Question

In terms of a positive constant k, random variables X and Y have joint PDF
[k+3x²
-1/251<1/2,
» - {*
fx,y (x, y) =
otherwise.
(a) What is k?
(b) What is the marginal PDF of X?
(c) What is the marginal PDF of Y?
(d) Are X and Y independent?

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