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Suppose that X1 and X2 are Bernoulli random variables with parameter 0. (a) Find two different joint distributions that (X1, X2) could have that would give these two marginal distributions. (b) When drawing a table for the joint pmf, the p(1, 1) entry will determine all the others (because of the given marginals). Find the best bounds for p(1, 1) in terms of 0 that you can. (c) Show that the only joint distribution that will make X1 and X2 uncorrelated will make p(1, 1) = 6°. In other words, if X1 and X2 are uncorrelated, then they are independent.

Suppose that X1 and X2 are Bernoulli random variables with parameter 0. (a) Find two different joint distributions that (X1, X2) could have that would give these two marginal distributions. (b) When drawing a table for the joint pmf, the p(1, 1) entry will determine all the others (because of the given marginals). Find the best bounds for p(1, 1) in terms of 0 that you can. (c) Show that the only joint distribution that will make X1 and X2 uncorrelated will make p(1, 1) = 6°. In other words, if X1 and X2 are uncorrelated, then they are independent.

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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7. Suppose that X1 and X2 are Bernoulli random variables with parameter 0. (a) Find two different joint distributions that (X1, X2) could have that would give these two marginal distributions. (b) When drawing a table for the joint pmf, the p(1, 1) entry will determine all the others (because of the given marginals). Find the best bounds for p(1, 1) in terms of 0 that you can. (c) Show that the only joint distribution that will make X1 and X2 uncorrelated will make p(1,1) = 62. In other words, if X1 and X2 are uncorrelated, then they are independent.
Transcribed Image Text:7. Suppose that X1 and X2 are Bernoulli random variables with parameter 0. (a) Find two different joint distributions that (X1, X2) could have that would give these two marginal distributions. (b) When drawing a table for the joint pmf, the p(1, 1) entry will determine all the others (because of the given marginals). Find the best bounds for p(1, 1) in terms of 0 that you can. (c) Show that the only joint distribution that will make X1 and X2 uncorrelated will make p(1,1) = 62. In other words, if X1 and X2 are uncorrelated, then they are independent.
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