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We consider a pair of continuous random variables (XY) whose joint density is give f(x, y) = {k(² + y²) si 1 ≤ x ≤5a-l≤y≤l et-1 0 Otherwise (a) For which value(s) of k does the function have a density? (b) Calculate the marginal densities of X and Y. (c) Are the variables X and Y independent? (d) Determine the marginal density of X given that Y=0. (e) Calculate the covariance of X and Y.

We consider a pair of continuous random variables (XY) whose joint density is give f(x, y) = {k(² + y²) si 1 ≤ x ≤5a-l≤y≤l et-1 0 Otherwise (a) For which value(s) of k does the function have a density? (b) Calculate the marginal densities of X and Y. (c) Are the variables X and Y independent? (d) Determine the marginal density of X given that Y=0. (e) Calculate the covariance of X and Y.

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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We consider a pair of continuous random variables (XY) whose joint density is given Sk(+²) sil≤x≤ 5 et-1 ≤ y ≤ 1 1⁰ Otherwise f(x, y) = (a) For which value(s) of k does the function have a density? (b) Calculate the marginal densities of X and Y. (c) Are the variables X and Y independent? (d) Determine the marginal density of X given that Y=0. (e) Calculate the covariance of X and Y.
Transcribed Image Text:We consider a pair of continuous random variables (XY) whose joint density is given Sk(+²) sil≤x≤ 5 et-1 ≤ y ≤ 1 1⁰ Otherwise f(x, y) = (a) For which value(s) of k does the function have a density? (b) Calculate the marginal densities of X and Y. (c) Are the variables X and Y independent? (d) Determine the marginal density of X given that Y=0. (e) Calculate the covariance of X and Y.
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