Statistics - Moment Generating Functions

  • #1

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If the moment generating function for the random variable X is M[X(t)] = 1/(1+t), what is the third moment of X about the point x = 2? The general formula only states how to find moments about x = 0. Thanks!
 

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  • #2
andrewkirk
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The n-th moment of X about a is defined as ##E[(X-a)^n]##.

Substitute n=3 and a=2 into that, then expand ##(X-a)^n## to polynomial form and substitute that into the above expression. You will get the sum of a bunch of moments about zero, which you can then use the MGF to calculate.
 
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  • #3
The n-th moment of X about a is defined as ##E[(X-a)^n]##.

Substitute n=3 and a=2 into that, then expand ##(X-a)^n## to polynomial form and substitute that into the above expression. You will get the sum of a bunch of moments about zero, which you can then use the MGF to calculate.
Ok I got it! Thanks so much! :)
 

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