R help - May 2009 - Bivariate pdf and marginal pdf of non-standard distributions

Hi,

I am trying to find marginal pdfs when joint pdf of two continuous variables is
given.

Simple case is like this: 

The joint pdf is

f(x,y) = 4xy, x lies between 0 and 1, and y also lies between 0 and 1.

I tried following crude way of doing it but it is not complete.

Could you post a suggestion to it. 
Thanks,
Jay Liu, University of Tennesse at Knoxville

##################
# f(x,y) = 4xy, range of x is (0,1), range of y is (0,1)
# Checking if f (x,y) is a joint pdf
Pxy<-integrate(function(y) { 
sapply(y, function(y) {
integrate(function(x) {
sapply(x, function(x) (4*x*y))
}, 0, 1)$value
})
}, 0, 1)
 
print("Value of int int f(x,y)dx dy")
Pxy
# To find marginal distribution, I tried this, but this is incorrect because x
is not all considered while integrating the joint pdf
 # Assume x to be a constant
# Px1 = f(x)
Px1<-integrate(function(y) { 
 4*y
}, 0, 1)$value


      
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