Hello, I have a question about conditional distributions in the continuous case.
We are given that the joint distribution function of two continuous random variables X and Y is
The marginal distribution of Y can be found by integrating with respect to x, the marginal distribution of Y is
The book asks to find the conditional density of X given that Y =.3
This is the answer that is listed in the book
Why is the book just plugging in the value .3 for y? Shouldn't we be integrating since this is continous?