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Please show some working when substituting the equation.

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  • $\begingroup$ please add the self-study tag for textbook questions $\endgroup$
    – Glen_b
    Commented Mar 31, 2013 at 8:58
  • $\begingroup$ 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. $\endgroup$
    – Glen_b
    Commented Mar 31, 2013 at 9:32
  • $\begingroup$ 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! $\endgroup$
    – user23672
    Commented Mar 31, 2013 at 9:44

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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

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  • $\begingroup$ 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 for example. $\endgroup$
    – Glen_b
    Commented Mar 31, 2013 at 9:08

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