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

Let X1,X2,...,Xn be a random sample from any distribution with mean μ and moment generating function M(t). Assume that M(t) is finite for some t > 0.

Let c>μ be any constant. Let Yn = X1+X2+···+Xn. Show that P(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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milcah answered 1 year ago

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