With reference to Theorem 3.3, verify that

(a) P(X > x_i) = 1- F(x_i) for i = 1, 2, 3, . . . , n;

(b) P(X G x_i) = 1- F(x_i- 1) for i = 2, 3, . . . , n, and P(X ≥ x₁) = 1.

Theorem 3.3

If the range of a random variable X consists of the values x₁ < x₂ < x₃ < · · · < x_n, then f(x₁) = F(x₁) and f(x_i) = F(x_i) – F(x_i – 1) for i = 2, 3, . . . , n