2.21 Suppose that n tn, n = 1, 2, . . . . Show that the...

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2.21 Suppose that ξn ∼ tn, n = 1, 2, . . . . Show that the following hold:

(i) ξn

−→d ξ ∼ N(0, 1).

(ii) mn(t) = E(etξn )=∞, ∀t = 0.

(iii) m(t) = E(etξ ) = et2/2, t ∈ R.

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