Reference no: EM132386854

Prove these statements or find a counterexample:

a) For any random variable X, E(X^2) >= E^2(X)

b) The median of a random variable X is invariant to shifts, i.e. the median of the random variable X + b for any constant b, equals median(X) + b

c) If X and Y have the same distribution and are independent, then E(XY) = E^2(X)

d) If X1, X2 and X3 have the same distribution, then E(X_1 / [X_1 + X_2 + X_3]) = 1/3