(Solved) Suppose that X is a standard normal random variable. Now we define a new random variable Y such that Y = a + bX + cX^2 . (a) Calculate the covariance...

Suppose that X is a standard normal random variable. Now we define a new random variable Y such that Y = a + bX + cX^2 .

(a) Calculate the covariance of X and Y ,

i.e., Cov(X, Y ). Hint: For a standard normal random variable, the m-th moment is

E(X^m) = 0, when m is odd,

=(2^(âˆ’m/2))(m! )/(m/2)! ), when m is even.

(b) Find the correlation coefficient Ï(X, Y )

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