1. ## Density Function

If X and Y are continuous random variables with joint probability density function

a) Calculate the marginal density function (fx) of X.

b)Determine whther or not X and Y are independent.

Would i be right in saying that part a) is 12x.
And that they are noy independent because their both marginal density functions multiply to 144xy.
Any guidance wold be great

2. Originally Posted by matty888
If X and Y are continuous random variables with joint probability density function

a) Calculate the marginal density function (fx) of X.

b)Determine whther or not X and Y are independent.

Would i be right in saying that part a) is 12x. Mr F says: No.
And that they are noy independent because their both marginal density functions multiply to 144xy.
Any guidance wold be great
$f_X(x) = \int_{y = 0}^{y = -x+1} 24xy \, dy = 12x(1-x)^2$.

It is evident from the region over which the joint pdf is non-zero that X and Y are NOT independent.