Question

Exercise 1. For any RV X and real numbers a,b ∈ R, show that E[aX +b]=aE[X]+b....

Exercise 1. For any RV X and real numbers a,b ∈ R, show that
E[aX +b]=aE[X]+b. (1)

Exercise2. LetX beaRV.ShowthatVar(X)=E[X2]−E[X]2.

Exercise 3 (Bernoulli RV). A RV X is a Bernoulli variable with (success) probability p ∈ [0,1] if it takes value 1 with probability p and 0 with probability 1−p. In this case we write X ∼ Bernoulli(p). ShowthatE(X)=p andVar(X)=p(1−p).

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