Suppose $p(x, y, z)$, the joint probability mass function of the random variables $X, Y$, and $Z$, is given by
$$
\begin{aligned}
& p(1,1,1)=\frac{1}{8}, \quad p(2,1,1)=\frac{1}{4}, \\
& p(1,1,2)=\frac{1}{8}, \quad p(2,1,2)=\frac{3}{16}, \\
& p(1,2,1)=\frac{1}{16}, \quad p(2,2,1)=0, \\
& p(1,2,2)=0, \quad p(2,2,2)=\frac{1}{4}
\end{aligned}
$$
What is $E[X \mid Y=2]$ ? What is $E[X \mid Y=2, Z=1]$ ?
Buonasera a tutti. Ho provato a svolgere questo esercizio, ma non mi trovo con la soluzione. Come lo devo risolvere? Grazie in anticipo.
