Let $Y$ be a Poisson $\lambda$ random variable, and define $X=I_{[Y>0]}$. Compute $E(Y\,|\,X)$ as a function of $X$ and find $E(|Y-X|)$.
So far, I found the mass function of $X$, $$f_X(x)=\begin{cases}
P(X=0)&=e^{-\lambda}\\
P(X=1)&= 1-e^{-\lambda}
\end{cases}$$
I don't see how to f...
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Q: $|G|=pq$, where $p$ and $q$ are primes, is the semidirect product of subgroups of orders $p$ and $q$
I am currently working on the following exercise:
Let $G$ be a group of order $pq$, where $p$ and $q$ are primes and $p > q$. Prove that $G = N \rtimes H$ for some subgroups $N$ and $H$ of orders $p$ and $q$, respectively.
Now, I just proved before this that for $G$ where $|G|=pq$ for $p$, ...
