Let X have mass function f(x)={0{x(x+1)}-1 . If x=1, 2, …, otherwise, and let α ∈ R. For what values of α is it the case that E(Xα) < ∞ ?

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Let X have mass function f(x)={₀^{x(x+1)}-1 . If x=1, 2, …, otherwise, and let α ∈ R. For what values of α is it the case that E(X^α) < ∞ ?

1. α < 1/2
2. α < 1
3. α > 1
4. α > 3/4

Correct Answer: α < 1

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