00:01
In this question, it is given that x has normal distribution.
00:14
Also, the expected value is 0 and variance equals 1.
00:29
In the question, it is given that w equals 1 or w equals minus 1 with probabilities 1 by 2 and y equals wx.
00:48
So we have to show that x and y are.
00:52
Uncorrelated.
00:54
So we have to consider the covariance xy is covariance of x, comma y equals expectation of xy minus expectation of x, expectation of y.
01:18
So by the definition of random variables, x, y and w and independent of w from x.
01:26
So there is so according to the independence rule we have this is equal expectation of x comma y minus 0.
01:42
So that is expectation of x square minus 0 which equals 0 hence the covariance of x y is 0 which means x and y are uncorrelated.
01:54
In the second question we have to find both x and y have the same normal distribution...