00:01
Hello students, as per the given question, it is given that the random variable are pairwise uncorrelated.
00:08
So, the correlation coefficient between two random variables is equal to their covariance divided by the product of their standard deviations.
00:15
So, the standard deviation for each variable is 1.
00:22
So, now we need to calculate the correlation coefficient between x1 plus x2 and x2 plus x3.
00:30
So, we have the formula that covariance of x1 plus x2 comma x2 plus x3 is equals to covariance of x1 comma x2 plus covariance of x1 comma x3 plus covariance of x2 comma x2 plus covariance of x2 comma x3.
01:05
So, since x2 is same variable in both the terms where covariance of x1 comma x2 is equals to 1, the other covariances are 0.
01:13
Since the variabilities are pairwise uncorrelated, so, correlation is equals to covariance of x1 plus x2 comma x2 plus x3 divided by 1 into 1.
01:37
Coming to the b bit where the correlation between x1 plus x2 and x3 plus x4.
01:46
So, for this we have covariance of x1 plus x2 comma x3 plus x4 is equals to covariance of x1 comma x3 plus covariance of x1 comma x4 plus covariance of x2 comma x3 plus covariance of x2 comma x4.
02:22
So, all the covariances are 0 since the variability are pairwise uncorrelated.
02:29
So, the correlation is equals to covariance of x1 plus x2 comma x3 plus x4 by 1 into 1, but all these values are equals to 0...