Question

If two random variables have the same generating function, must they have the same cumulative distribution function? L.8) Central Limit Theorem One version of Central Limit Theorem says this: Go with independent random variables (Xi, X2, X3, ..., X.....] all with the same cumulative distribution function so that: 11-Expect[Xi]-Expect[s] and σ. varpk-VarX] for all i and j . Put: s[n] = As n gets large, the cumulative distribution function of S[n] is well approximated by the Normal[o, 1] cumulative distribution function. You prove this by setting G[tl-Expecte and a rguing why: G[tr→a certain function h[t] as n→oo What is that certain function, h[t]?

Answer 1

$G[t]^n\rightarrow exp(t^2/2)~which~is~a~moment~generating~function~of~N(0,1).\\ Hence~h(t)=e^{t^2/2}$