00:01
Hi, i'm david and i'm here to help you answer your question.
00:03
Now let me bring up your question here.
00:07
In this question here we want to reveal about the shown probability density function of the two random variables.
00:14
Now the question asks you find the marginal density of each of them.
00:20
Now let me do the one first to find the marginal density of the x, which you need to do integrating over the one.
00:32
And then f x y from minus infinity to infinity so now y goes from the zero to infinity so we have the zero to infinity inside we have the six each of the power minus two x minus three y and then from here we see we have the e to the power minus two x will be the constant and can bring outside inside we have the integral from zero to infinity six and we will can write the 6 as the 2 and then 3 you can put it inside.
01:08
The reason why because now i will have exactly that will be the untidy derivative now.
01:14
So we get equal to 2 e to the bar minus 2x and then untidy derivative you get equal to the e to the bar minus 3y.
01:24
This will be the minus here and then we get it will be evaluating from the 0 to infinity.
01:34
And the infinity in same gone the zero and the zero we got equal to the one...