The moment generating function (MGF) for the random variable X is given as M[X(t)] = 1/(1+t). To find the third moment of X about the point x = 2, substitute n=3 and a=2 into the formula E[(X-a)^n]. Expand (X-a)^n to polynomial form and substitute into the expression to obtain the sum of moments about zero, which can then be calculated using the MGF.
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andrewkirk said: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.