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Let X and Y be continuous random variables having the joint pdf [8ay, 0

Let X and Y be continuous random variables having the joint pdf [8ay, 0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let X and Y be continuous random variables having the joint pdf 8xy, 0≤ y ≤ x ≤1 0, otherwise. f(x, y) = (a) Sketch the graph of the support of X and Y. (b) Find ƒ₁(x), the marginal pdf of X. (c) Find ƒ₂(y), the marginal pdf of Y. (d) Compute μx, μy, o, o, Cov(X, Y), and p. (e) Find g(x|y =), the conditional pdf of X given Y = 3. (f) Find P(X < ³|Y = }). (g) Are X and Y independent? Why or why not?
Transcribed Image Text:Let X and Y be continuous random variables having the joint pdf 8xy, 0≤ y ≤ x ≤1 0, otherwise. f(x, y) = (a) Sketch the graph of the support of X and Y. (b) Find ƒ₁(x), the marginal pdf of X. (c) Find ƒ₂(y), the marginal pdf of Y. (d) Compute μx, μy, o, o, Cov(X, Y), and p. (e) Find g(x|y =), the conditional pdf of X given Y = 3. (f) Find P(X < ³|Y = }). (g) Are X and Y independent? Why or why not?
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