Let (X; Y ) have joint mass function $P(k, n) = \frac {C*2^-k}{n}$ , for k = 1, 2, and n = 1, 2, , k, and suitable constant C. Compute $E(X|Y = y)$.
Its easy to calculate the $P(X,Y)$ but i am getting confused in calculating $P(Y)$ also what should be the value(range) of X. Can someone please provide some direction?
The conditional distribution of $X$ is $$p_{X|Y=y}(x) = \frac{p_{X,Y}(x,y)}{p_Y(y)}=\frac{P((X,y)=(x,y))}{P(Y=y)}.$$ You know the numerator already. The denominator can be found by partitioning the event $Y=y$ on the value of $X$: $$P(Y=y)=\sum_{k=1}^2 P(Y=y \text{ and } X=x).$$ Finally, $E(X \mid Y=y)= \sum_{k=1}^2 x \cdot p_{X|Y=y}(x)$. The sum is over $k=1,2$ because according to the formula you gave, $X$ only takes on the values $1$ or $2$.