Lecture 8 : Linearity of expectation
نویسنده
چکیده
1 Linearity of expectation Now let us see some extensions of the basic method. Theorem 1 (Linearity of expectation). Let X1, · · · , Xn be random variables and X = c1X1+ · · ·+ cnXn, where ci’s are constants. Then EX = c1 EX1 + · · ·+ cn EXn. Proof. We prove it by induction. The base case of n = 1 is trivial. For the inductive step, it is sufficient to show that E[X + Y ] = E[X] + E[Y ] for two random variables X and Y . Indeed, E[X + Y ] = ∑
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