Q6(b) Let Y₂ ~ x² (n). The goal is to find the limiting distribution of Zn = (Yn-n) √2n as n →∞0. First, express the moment-generating function Mz, (t) of Zn in terms of the moment-generating function My, (t) of Yn. Then find ln(Mz„ (t). Use the fact ln(1 − x) = −x − x² /2 - x³/3 - x²/4 to show that as n → ∞, Mz, (t) converges to et²/2 and hence Zn converges to N(0, 1) as n → ∞o.

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