# Thread: Joint PDF explaining question

1. ## Joint PDF explaining question

Hiya

Got a question on joint density of two voltages:

f(x,y) = {2, {0<x<1}and{0<y<1-x} 0, otherwise

So I drew what I thought was f(x,y) in plan view (the region {0<x<1}and{0<y<1-x}). Is this correct?
Next question was tow explain if the voltages x and y are independent. It seems to me that they can't be because the joint PDF depends on both x AND y, where as if they were independent it would depend on x OR y. I understand the idea of statistical independence, but not how it translates in the maths.

Thanks very much in advance for any help.

2. ## Re: Joint PDF explaining question

Independence of the two rVars $\displaystyle X,Y$ corresponds with $\displaystyle F (x,y) = F_x (x) F_y (y)$ being true.
That is, the random variables are said to be independent if their joint CDF factors into the product of their marginal CDF's. (ref:Rice (2007))
So, I think you should be able to find the marginals and then do a check to see if they are indeed independent.

(I am also learning this stuff at the moment, so don't take my word as absolute truth...)