I recently learned of probability generation functions and that the sum of two independent random variables can be found out by multiplying the PGFs. I wanted to know if anything similar can be done for the difference.
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asked Dec 30, 2019 at 4:32
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Yes, you can, let $A=X-Y$ and $G_X(z),G_Y(z)$ be PGFs of $X,Y$ respectively, then: $$G_A(z)=E[z^{X-Y}]=E[z^X]E[(1/z)^Y]=G_X(z)G_Y(1/z)$$
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$\begingroup$ Thank you very much!! $\endgroup$ Commented Dec 30, 2019 at 5:23
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$\begingroup$ I tried up voting, but it said votes cast by people with less than 15 reputation are recorded but not publicly displayed!! $\endgroup$ Commented Dec 31, 2019 at 6:03
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$\begingroup$ thanks, you can accept the answer by clicking the tick sign under the arrow in my answer $\endgroup$– gunesCommented Dec 31, 2019 at 6:40
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$\begingroup$ Done!! Thank you again. $\endgroup$ Commented Dec 31, 2019 at 10:43