An actuary determines that the claim size for a certain class of accidents is a random variable, X?

with moment generating function
MX(t) =1/(1 - 2500t)^4 :
Determine the standard deviation of the claim size for this class of accidents.

Answer by cidyah
Mx(t) = (1-2500t)^(-4)
Mx'(t) = (-4)(1-2500t)^(-5) (-2500) = 10,000 / (1-2500t)^5
Let t=0
E(x) =10,000
Mx''(t) = 10000(-5)(1-2500t)^(-6)(-2500)
=125,000,000 / (1-2500t)^6
Let t=0
125,000,000
Variance = E(x^2) - E^2(x) = 125,000,000 - 10,000^2
=25,000,000
Standard deviation = sqrt(25,000,000)=5,000

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Orignal From: An actuary determines that the claim size for a certain class of accidents is a random variable, X?