I have two i.i.d. binomial variables X and Y with given n and p. What is probability mass function of product of X and Y?
2026-05-05 05:49:05.1777960145
Probability mass function of product of two binomial variables
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I doubt if there is a simple expression. To get started $P(XY=0)=P(X)=0+P(Y)=0-P(X=0)P(Y=0)$, $P(XY=1)=P(X=1)P(Y=1)$, $P(XY=2)=P(X=1)P(Y=2)+P(X=2)P(Y=1)$. The general term for$P(XY=k)$ then depends on the factoring of $k$.