Let X be a standard normal random variable and set Y = exp(X). Show that the rth
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Let X be a standard normal random variable and set Y = exp(X). Show that the rth moment of Y about the origin is μ′r = exp(r2
/2). Hence find expressions for the first four cumulants of Y. Show that the series expansions for ΜY(ξ) and KY(ξ) about ξ = 0 are divergent for all real ξ> 0 even though all cumulants are finite (Heyde, 1963)
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Related Book For 
Tensor Methods In Statistics Monographs On Statistics And Applied Probability
ISBN: 9781315898018
1st Edition
Authors: Peter McCullagh
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