Prove that E[X2] ≥ (E[X])2. When do we have equality?
Let c be a constant. Show that
(a) Var(cX) = c2Var(X);
(b) Var(c + X) = Var(X).
(a) Calculate E[X] for the maximum random variable of Exercise 37.
(b) Calculate E[X] for X as in Exercise 33.
(c) Calculate E[X] for X as in Exercise 34.
If X is uniform over (0, 1), calculate E[Xn] and Var(Xn).
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