Question: 6.5 Suppose X has the density f(x) = a xa+1 1(x>1) where a > 0. This distribution is called a Pareto distribution or a power

6.5 Suppose X has the density f(x) = a xa+1 1(x>1)

where a > 0. This distribution is called a Pareto distribution or a power law distribution.

a) Show that MX(t) = ∞ for every t ∈ R.

b) Show that EXn < ∞

if and only if a>n.

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