11-2-2010, 03:44 PM | #1 | |
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[Graduate Studies - Actuarial Math] - Distribution/Density functions
I haven't the foggiest idea how to go about solving these problems. Any assistance would be awesome.
[note: the "x" in Mx(t) is a subscript] 1) Let Mx(t) is the moment generating function of a random variable X. Let R(t) = ln(Mx(t)). Then prove that i) R'(0) = µ ii) R''(0) = σ^2 Find R(t) if X is a standard normal variate and show the above results. 2) Let f(x) = 2g(x)G(λx). -∞<X<∞. Where g(x) and G(x) are the density and distribution function of the standard normal distribution respectively. Is f(x) a density function? If yes, find the mean of the distribution.
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