00:01
In this question we are given that the joint probability density function of x and y is given as if x comma y is equals to 6 upon 7 x square plus x y by 2.
00:38
Now we are given four parts.
00:40
So in the first part we have to find the value of c.
00:44
So the total probability should be 1.
00:56
So if x comma y, d x, dyx ,dy is equals to 1.
01:05
So it is from 0 to c and it is 0 to 2.
01:13
So it is 6 upon 7.
01:15
X is square plus xy by 2, dy into d x is equal to 1.
01:22
So 6 upon 7 is constant.
01:28
So from 0 to 2 it is x square plus xy by 2.
01:37
D .y.
01:38
D x is equals to 1.
01:42
So this will be 6 upon 7 0 to c.
01:50
X square y plus x y square upon 4.
01:55
0 2 d x is equal to 1.
02:03
So it is from 0 to c 2x square plus x 2 square up on 4 minus 0 minus 0 d x is equal to 1.
02:24
So 6 upon 7 0 to c 2x square plus x d x is equal to 1.
02:35
6 upon 7 2x cube by 3 plus x square by 2 0 to c is equal to 1.
02:47
So it is 6 upon 7 2c cube by 3 plus c square upon 2 is equal to 1.
02:57
6 upon 7 it is 4 c cube plus 3 c square upon 6 is equal to 1.
03:04
So 4c cube plus 3c square is equal to 7...