Sampling from a distribution with given pdf Given a continuous multivariate pdf in analytical form (i.e. in function form), how can one sample from the corresponding distribution? In other words, what are the ways of coming up with random (or psuedo-random) realizations from the distribution with probability matching the one corresponding to the given pdf? What is the general idea/principle behind the sampling procedure? 
Referring to related references would be helpful too.

Generate a random number $x$ and output the smallest $y$ such that $F(y) \ge x$ where $F$ is the cdf of your distribution? What are you looking for exactly?
