I have random variables X and Y. X is chosen randomly from the interval (0,1) and Y is chosen randomly from (0, x). I want to calculate the conditional PDF of Y given X. I want to do this by calculating the joint PDF of X and Y and dividing that by the marginal PDF of X.
The marginal PDF of X is simply 1, since we're equally likely to pick a number from the range of (0,1). We can verify this using calculus by taking the derivative of the CDF, which is simply F(X <= x) = x/1, or x. The derivative of xdx = 1.
I'm struggling with the joint PDF. I have a strong feeling it's 1/x, however I'd like some advice on how to get it.