Exercise 3.23 Let X and Y be independent discrete random variables. Prove that P(X ≥ x and Y ≥ y) = P(X ≥ x)P(Y ≥ y)

for all x, y ∈ R.

Exercise 3.24 The indicator function of an event A is the function 1A defined by 1A(ω) =

(

1 if ω ∈ A, 0 if ω /∈ A.