Question: X and Z are independent random variables with E[X] = E[Z] = 0 and variance Var [X] = 1 and Var [Z] = 16. Let

X and Z are independent random variables with E[X] = E[Z] = 0 and variance Var [X] = 1 and Var [Z] = 16. Let Y = X + Z. Find the correlation coefficient p of x and Y, Are X and Y independent?

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