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With reference to Theorem 3 3 verify that a P X xi

With reference to Theorem 3.3, verify that

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

(b) P(X G xi) = 1- F(xi- 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 < · · · < xn, then f(x1) = F(x1) and f(xi) = F(xi) – F(xi – 1) for i = 2, 3, . . . , n

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

(b) P(X G xi) = 1- F(xi- 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 < · · · < xn, then f(x1) = F(x1) and f(xi) = F(xi) – F(xi – 1) for i = 2, 3, . . . , n

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