Unformatted text preview: X = 1 + b log U/ log q c ∼ Geometric( q ) . Here b x c stands for the greatest integer less than or equal to x . 8. Let X ∼ Binomial ( n, p ) consider E eX/n = ( pe1 /n + 1p ) n (later on you will see this result via the moment generating function). Let n = 10 and p = 1 / 100 and use the Taylor expansion up to the fourth order to approximate E eX with functions of the ﬁrst four moments of X , what is your error? ( hint: You may ﬁnd the formulation given in Ch. 4 of Ross for the k th moment of a binomial r.v. via a recursive formula useful. ) 1...
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 Spring '07
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 Normal Distribution, Probability, Probability theory, Ross Page

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