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Suppose that, for some h > 0 , non-degenerate X has finite moment generating function M X ( t ) = E [ exp (

Suppose that, for some h>0, non-degenerateX has finite moment generating function MX(t)=E[exp(tX)]for t(h,h). Let =E[X].

a) Show thatMX(t)exp[t] for t(h,h), with equality only at t=0.

b) Show that MX(t) is convex on (h,h).

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