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3. Let fcr'y if0 < x≤ 1,0 ≤ y ≤ 1 otherwise f(x) = - {c²%² Find the following: a. c such that f(x, y) is a probability density function. b. The marginal distributions of X and Y. c. Expected values of X and Y. d. Variances of X and Y.. e. Covariance of X and Y. f. The conditional distribution of X given Y = y and the conditional distribution of Y given X = x. g. Are X and Y independent? How do you know?

3. Let fcr'y if0 < x≤ 1,0 ≤ y ≤ 1 otherwise f(x) = - {c²%² Find the following: a. c such that f(x, y) is a probability density function. b. The marginal distributions of X and Y. c. Expected values of X and Y. d. Variances of X and Y.. e. Covariance of X and Y. f. The conditional distribution of X given Y = y and the conditional distribution of Y given X = x. g. Are X and Y independent? How do you know?

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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3. Let Sca'y if0≤x≤ 1,0 ≤ y ≤1 f(x) = otherwise Find the following: a. c such that f(x, y) is a probability density function. b. The marginal distributions of X and Y. c. Expected values of X and Y. d. Variances of X and Y.. e. Covariance of X and Y. f. The conditional distribution of X given Y g. Are X and Y independent? How do you know? = y and the conditional distribution of Y given X = x.
Transcribed Image Text:3. Let Sca'y if0≤x≤ 1,0 ≤ y ≤1 f(x) = otherwise Find the following: a. c such that f(x, y) is a probability density function. b. The marginal distributions of X and Y. c. Expected values of X and Y. d. Variances of X and Y.. e. Covariance of X and Y. f. The conditional distribution of X given Y g. Are X and Y independent? How do you know? = y and the conditional distribution of Y given X = x.
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