00:02
Hi, here it is given that we have two random variables, x and y, variance of x is 4 and variance of y is 2.
00:12
Now, we have to find the correlation coefficient between these two random variables x and y, where variance of x plus twice y is given is equal to 50.
00:24
Okay, so two random variables, x and y, where, it is given variance of x is equals to 4 and variance of y is equals to 2 these two values are given it is also given that variance of twice x plus y right sorry x plus twice y x plus twice y variance of x plus twice y is given is equal to 15 now, from here, variance of x plus twice, twice y means variance of x plus variance of twice y plus twice covariance of x comma twice y is equal to 15.
01:28
Now, this is equal to variance of x, that means 4 plus see variance of twice y, 2 is inside the variance and it comes out as a square.
01:40
So two square means four into variance of y, variance of y is two.
01:43
So, four into two plus two into covariance of x, comma twice.
01:48
So i means, see, these two comes out.
01:51
So two into two, covariance of xy is equals to 15.
01:59
Now, this is four into two, eight plus four, twelve.
02:02
So this is 2 into 4, 4 covariance xy is equals to 15 minus 4 plus 8, 12...