(Solved): Problem 1 ( 7 points). Given p(0;1), let X1 and X2 be independent Bernoulli (p) distrib ...
Problem 1 ( 7 points). Given p?(0;1), let X1? and X2? be independent Bernoulli (p)? distributed random variables. For i?{1,2}, let the random variable Yi? be defined by Yi?=2X1??1. For some p?(?1;1)\{0} let Z=pY1?+1?p2?Y2?. Compute the expectation and the variance of Z as well as the correlation of the random variables Z and Y2?.