Suppose X is a discrete random variable with range {0,1, 2}, such that 1. and P(X...

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Suppose X is a discrete random variable with range {0,1, 2}, such that 1. and P(X = 2) = d P(X = 0) = P(X = 1) = %3D %3D %3D %3D 6' 3' (a) Determine the value of the constant d. (b) Calculate E(X") for each value 1 <n< 6. (c) Calculate Var(X") for each value 1<n<3. (d) Can checking covariance be used to prove the independence of two random variables? (e) Are random variables X, X2 and X mutually independent? Jus- tify your answer. (f) Calculate Var(X + X? + X3). Suppose X is a discrete random variable with range {0,1, 2}, such that 1. and P(X = 2) = d P(X = 0) = P(X = 1) = %3D %3D %3D %3D 6' 3' (a) Determine the value of the constant d. (b) Calculate E(X") for each value 1 <n< 6. (c) Calculate Var(X") for each value 1<n<3. (d) Can checking covariance be used to prove the independence of two random variables? (e) Are random variables X, X2 and X mutually independent? Jus- tify your answer. (f) Calculate Var(X + X? + X3).