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(Solved): Problem 1 ( 7 points). Given p(0;1), let X1 and X2 be independent Bernoulli (p) distrib ...




Problem 1 ( 7 points). Given \( p \in(0 ; 1) \), let \( X_{1} \) and \( X_{2} \) be independent Bernoulli \( (p)- \) distribu
Problem 1 ( 7 points). Given , let and be independent Bernoulli distributed random variables. For , let the random variable be defined by . For some let . Compute the expectation and the variance of as well as the correlation of the random variables and .


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It is given that X1,X2 are independent Bernoulli(p)-distributed random variables, So, E(X1)=p=E(X2) and Var(X1)=p(1?p)=Var(X2)Now, Yi=2Xi?1So, Y1=2X1
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