Prove that E[X 2 ] ≥ (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...


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).




May 08, 2022
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