00:01
Okay, so we need to show first that the covariance of x, y, which is equal to expected value of x, y minus expected value of x times expected value of y is equal to zero.
00:21
Now, for this part, we have e of x is equal to zero because of the mirror symmetry with respect to the y -axis and e y is zero for the same reasons or due to symmetry about the x -axis because symmetry.
00:50
Now, for this part, e of x, y, this is zero because the product x, y has a magnitude that is four -fourths symmetric in the four quadrants.
01:07
So let's say this is y -axis, this is x -axis, this is positive and this is negative and this is positive and this would be negative, the value of x, y.
01:32
So whatever the joint density function f x, y looks like, so that is e of x, y by definition is x, y and the joint density function.
01:50
This is going to have the four parts that cancel exactly...