11 Let X be a random variable with the probability density function f (x) 1 (1 x2) , x Prove that E X converges if 0 1 and diverges if 1

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Question: 11. Let X be a random variable with the probability density function f (x) = 1 (1 + x2) , < x < .

11. Let X be a random variable with the probability density function f (x) = 1 π(1 + x2) , −∞ < x < ∞. Prove that E ! |X| α" converges if 0 < α < 1 and diverges if α ≥ 1.

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