Question: (b) f has finite moments of all orders, (c) fa and f have equal moments of all orders, in that Z xk f

(b) f has finite moments of all orders,

(c) fa and f have equal moments of all orders, in that Z

∞

−∞

xk f (x) dx =

Z

∞

−∞

xk fa(x) dx for k = 1, 2, . . . .

Thus, { fa : −1 ≤ a ≤ 1} is a collection of distinct density functions having the same moments.

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