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Suppose that X1,...,XN are i.i.d. exponentially distributed random variables. Now assume that:

[tex]\mathcal{X}=\sum_n\frac{1}{1+a\,X_n}[/tex]

I need to find the CDF of X. I did the following:

1- Find the the CDF of Xi.

2- Find the CDF of 1+a X_i.

3- Find the CDF and PDF of 1/(1+a Xi).

4- The MGF of X is the product of the MGFs of the individual MGFs.

5- Take the inverse laplace transform of the total MGF divided by the Laplace variable s.

Are these steps valid?

Thanks

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# Can I do this transformation?

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