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Please show some working when substituting the equation.

Alexis
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user23672
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  • please add the `self-study` tag for textbook questions – Glen_b Mar 31 '13 at 08:58
  • Please don't radically alter your question in a way that makes answers to what you originally asked no longer an answer - the form of the original was fine, but now my answer doesn't look like it responds to your question - people would rightly downvote my answer on that basis. You can add followup questions or clarifications without changing the question quite so much. Your new question is basic mathematics and isn't on topic here; it's *exactly* like changing from $\sum_{i=1}^n x_i$ to $\sum_{j=1}^n x_j$ -- changing the dummy variable doesn't alter anything. – Glen_b Mar 31 '13 at 09:32
  • Sorry, cause I was unable to type out the math equations through the text box.. I change back the question. I am sorry, Thanks anw! – user23672 Mar 31 '13 at 09:44

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Actually, @DilipSarwate explained exactly how to do it in your previous question.

\begin{align} M_Z(t) &= E[e^{sZ}] \\ &= \int_{-\infty}^\infty e^{tz}\, f_Z(z) dz \\ &= \int_{-\infty}^\infty e^{tz}\, [pf_X(z)+(1-p)f_Y(z)] dz \end{align}

and then use basic properties of expectations / integrals

Glen_b
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  • Note that the argument in a mixture is going to be the same ($z$ in this case), even though the subscript that denotes the *form* of the density is different. See [here](http://en.wikipedia.org/wiki/Mixture_distribution#Finite_and_countable_mixtures) for example. – Glen_b Mar 31 '13 at 09:08