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  3. let x1,x2,...,xn be a random sample from any distr

Let X1,X2,...,Xn be a random sample from any distribution with mean ? and moment generating function...

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Basic Math

Let X1,X2,...,Xn be a random sample from any distribution withmean ? and moment generating function M(t). Assume that M(t) isfinite for some t > 0.

Let c>? be any constant. Let Yn = X1+X2+···+Xn. Show thatP(Yn ? cn) ? exp[?n a(c)] where P(Yn ? cn) ? exp[?n a(c)]

a(c) = sup[ct ? ln M (t)]. t > 0

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