Let $X$ and $Y$ have the joint pmf defined by $f(0, 0) = f(1, 2) = 0.3$, $f(0, 1) = f(1, 1) =0.2$
$(a)$ Tabulate the conditional pmf of $Y$ given $X=0$
$(b)$ Tabulate the conditional pmf of $X$ given $Y=2$
I know that this would mean for part $(a)$, I would need to find (and tabulate)
$f_{Y|X}(0|x=0)$
$f_{Y|X}(1|x=0)$
$f_{Y|X}(2
|x=0)$
And adding these up should equal to $1$.
But $f_{Y|X}(y,x) = \frac{f(x,y)}{f_X(x)}$. And what $f(x,y)$ and $f_X(x)$ are is unclear to me from the question. Anyone know how to find these? Thanks in advance.
Best Answer
I'm pretty sure $f_X(x)$ is the probability of $x$ equal to some value. $f(x,y)$ should be one of the values of the joint pmf that you listed. So for example, $f_{Y|X}(0 | x=0) = \frac{f(0,0)}{f_X(0)} = \frac{0.3}{f(0,0)+f(0,1)+f(0,2)} = \frac{0.3}{0.3+0.2+0} = 0.6$.