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 we're given the term bdf fxy equal to the 24 x power 3y for the x greater than 0 smaller than y smaller than 1.
00:20
Now once you find the marginal pdf on the x and y, let's try to find the marginal the bdf on the x, it's equal to the integral of the fxy over the y.
00:35
And here x equals from the 0 up to the y.
00:41
And y goes from the x up to 1.
00:45
So therefore we have x up to the 1.
00:48
So we have here 24x power 3 will be the constant we can bring outside integral x to 1, y, d, y.
00:58
So we have a 24 x power 3.
01:01
Untidy derivative of the y will be y square over 2 from x to 1.
01:07
So we have the 24 x power 3.
01:10
Now if we put the 1, this one will be divided by 2, so we have here will be 12.
01:17
And then you can put the 1 inside, we have the 1 minus x square.
01:21
And here x will be between the 0 and 1.
01:26
Now, f on the y, we should get the integral.
01:34
Y goes from, and we have to do the derivative which is much in the x, and the integral is split to the x and x goes from zero to the y.
01:44
We have a 24 x power 3 y.
01:48
Again, 24 1 will be the constant.
01:51
In 7 we have 0 to y, x power 3 the x.
01:55
We know that anti -derivative of the x power 3 could be x power 4.
01:59
Or over 4 from 0 to y...