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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
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