Need help solving this

The moment generating function of a random variable is given by

M_{X}(t)=(1/6)e^{t}+(1/3)e^{2t}+(1/2)e^{3t.}

a) Find the distribution function of x.

b) Find E(X).

any input highly appreciated.

thx

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- May 5th 2006, 11:53 PMredimoment generation function
Need help solving this

The moment generating function of a random variable is given by

M_{X}(t)=(1/6)e^{t}+(1/3)e^{2t}+(1/2)e^{3t.}

a) Find the distribution function of x.

b) Find E(X).

any input highly appreciated.

thx - May 6th 2006, 01:06 AMrgep
The moment generating function of

*X*is the function of*t*given by the expectation of . Expanded as a power series in*t*, the coefficient of is where is the*r*-th moment.

So the expectation of*X*, which is , is the coefficient of*t*in or alternatively .

To recover*X*we see that the random variable which takes values 1, 2, 3 with probabilities 1/6, 1/3, 1/2 respectively has the required MGF.

There's a good article in MathWorld. - May 6th 2006, 06:53 AMredi
thanks rgep