Let $X_n$ be an i.i.d. sequence of Poisson random variables with parameter $1$. Define $Y_0 = 1$ and $Y_n := X_nY_{n-1}$ for $n\geq 1$. How to show that $Y_n$ converges to $0$ almost surely, please? I think it is helpful to know the distribution of $Y_n$. However, how to find this out, please? Thank you!
2026-03-28 01:24:04.1774661044
What is the distribution of $Y_n$ and its convergency
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