Question: (10) Let X and Y be random variables such that Var(X) = 4, Var(Y) = 2, and Var(X+2Y) = 15. Determine the correlation coefficient

(10) Let X and Y be random variables such that Var(X) =

(10) Let X and Y be random variables such that Var(X) = 4, Var(Y) = 2, and Var(X+2Y) = 15. Determine the correlation coefficient of X and Y. (11) Prove that (a) sum of r independent geometric random variables each with parameter p is a negative binomial random variable with the parameters (r,p).. (b) the sum of two independent binomial random variables with the parameters (n1,p) and n2, p) is a binomial random variable with the parameters (n +n2,p). 1

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