Question

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4. Expectation of Product of Random Variables Proof From the definition of the expected value, the expected value of the product of two random variables is ı r P(X Y r2) E(X- Y) ri r2 where the sum is over all possible values of rı and r2 that the variable X and Y can take on (a) Using the definition above formally prove that if the events X = r1 and Y = r2 are independent (for any ri and r2), we have E(X Y) E(X E(Y) (b) Now, if you have two random variables X and Y and = a Xc, Y show that if E[X2]E[X]2, then E(X Y)E(X) E(Y) (c) If you roll a die 6 times in a row, what is the expected value of the product of the 6 outcomes?

Answer 1

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