Two continuous random variables $X $and $Y$ have the joint density $f(x,y) = C(x^2 + y), -1 \leqslant x \leqslant 1, 0 \leqslant y \leqslant 1.$
- Compute the constant $C$.
- Compute the probability $P(\{Y<0.6\})$.
- Compute the probability $P({Y<0.6\mid X=0.5})$.
To find $C$ I'm thinking I should solve for $C$ when the indefinite integral of $f(x,y) = 1$.
As far as finding the probability in part 2 I'm thinking of finding the integral of $f(x,y)$ with respect to $C$ from $0.0$ to $0.6$.
Part three I am not sure of. Can anyone point me in the right direction, not looking for answers as much as an understandable solution.