Question: Problem 3.12 The random variable X has the pf defined by f(x) = 1 x(x + 1) for x = 1, 2, . . .

Problem 3.12 The random variable X has the pf defined by f(x) = 1 x(x + 1) for x = 1, 2, . . . , n, . . . .

(a) Show that 1≤x<∞ 1 x(x+1) = 1. Hint: Use the algebraic identity: 1 x(x + 1) = 1 x − 1 x + 1 .

(b) Show that F(x) = P(X ≤ x) = x x + 1 for x = 1, 2, . . . , n, . . . .

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