Statistics Solutions

Solution: Two random variables X and Y are uncorrelated if Cov;(X, Y)=0. It is true that independent random variables are uncorrelated but uncorrelated random

Question: Two random variables \(X\) and \(Y\) are uncorrelated if \(\operatorname{Cov}(X, Y)=0\). It is true that independent random variables are uncorrelated but uncorrelated random variables may not be independent. Show that if \(\mathrm{X}\) and \(\mathrm{Y}\) are Bernoulli random variables and \(\operatorname{Cov}(X, Y)=0\) then \(\mathrm{X}\) and \(\mathrm{Y}\) are independent.

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