Continuous Distributions
Similarly for continuous random variables, the conditional probability density function of Y given (the occurrence of) the value x of X, can be written as
where fX,Y(x, y) gives the joint density of X and Y, while fX(x) gives the marginal density for X. Also in this case it is necessary that .
The relation with the probability distribution of X given Y is given by:
The concept of the conditional distribution of a continuous random variable is not as intuitive as it might seem: Borel's paradox shows that conditional probability density functions need not be invariant under coordinate transformations.
Read more about this topic: Conditional Probability Distribution
Famous quotes containing the word continuous:
“There is no such thing as a life of passion any more than a continuous earthquake, or an eternal fever. Besides, who would ever shave themselves in such a state?”
—George Gordon Noel Byron (1788–1824)