# Marginal PDF from Joint PDF

by JamieL
Tags: joint pdf, marginal pdf, pdf, pdf cdf normal dist
 P: 4 Hi all, I'm looking at the joint pdf F(x,y) = (8+xy^3)/64) for -1
P: 3,173
 Quote by JamieL Hi all, As far as I can tell, X and Y don't seem to depend on each other in this sense; i.e. for marginal(X) i would have Integral([JointPDF]dy), from -2 to 2, which comes out to 1/2.
How did you get the integral with respect to y to come out to be a constant? It should be a function of x.
 P: 4 Maybe I'm mistaking, but as far as I can tell the indefinite integral comes out to: (8y+(xy^4)/4)/64 + c. If you evaluate this from -2 to 2, the x terms cancel because the y is an even function, i.e. from -2 to 2 we get [(1/4)+16x]-[-(1/4)+16x], so (1/4)+(1/4)+16x-16x = 1/2. This is what made me think that perhaps my bounds are incorrectly calculated... Am I doing something wrong?
P: 3,173

## Marginal PDF from Joint PDF

 Quote by JamieL .. Am I doing something wrong?
Not in the integration. (I'm the one who was confused about that.) But the fact that the conditional distributions are constant (and thus "independent" of the values of both variables) doesn't show that the x and y are independent random variables. If x and y were independent random variables then for each pair of sets $A,B$ that define events $Pr(x \in A) = Pr(x \in A | y \in B)$

For example, consider the events $A = \{x: x \in [0, 1]\},\ B = \{y: y \in [0,1]\}$
 P: 3 Still, what would the bounds be? A marginal pdf should not be a constant