Thread: Joint probability function

I understand all the concepts of joint PDFs but I just can't get the right answer to this one. The function is:

f(x,y)=3x^(1/2)e^(-2y)

I need to find the probabilty over these two regions:

a) P (0 ≤ x ≤ 1; 3 ≤ y ≤ )
b) P({P ({(x, y) | 2/3 ≤ x ≤ 1; 0 ≤ y ≤ )
2

Explanations would be much appreciated. Thanks

Hello,

Originally Posted by notecardheart

I understand all the concepts of joint PDFs but I just can't get the right answer to this one. The function is:

f(x,y)=3x^(1/2)e^(-2y)

I need to find the probabilty over these two regions:

a) P (0 ≤ x ≤ 1; 3 ≤ y ≤ )
b) P({P ({(x, y) | 2/3 ≤ x ≤ 1; 0 ≤ y ≤ )
2

Explanations would be much appreciated. Thanks

By using wise definitions of the cumulative density functions, you should understand

, where is the pdf of X

For a joint distribution, it's the same reasoning :


So for the first one for example, it's

I would like to know the support of this joint density.
The rvs seem to be independent.