Hey, im a first year in leeds uni doing maths and there are some things im starting to get quiet stressed over and they arnt even hard so you'll probably see quite a few of my posts pop up with my exams coming in a few days.
The question im stuck on is:
Let X1 , X2 and X3 be independent random variables with zero mean and variance 1.
Find the correlation coefficient between Y1 = 2(X1) + (X2) and Y2 = (X2) ¡ 2(X3) .
I really dont know where to start and its quite conserning because i dont think its even hard .
I beleive that cov(x,y) = E(XY) -E(X)E(Y) but with a zero mean of the variables im unsure how this works. Thanks for all help.
Thankyou. Though i am confused. The question says the random variables are independent, doesn't that mean the correlation coefficient is 0? the answer to the question is 0.2.
E(xy) = E(x)E(y) doesn't it when they are independent?
This gives E(y1) = 2E(x1) + E(x2) and E(y2) = E(x2) - 2E(x3) but the question states the mean of all these random variables is 0 thus that gives 0 for both of them. But the answer is 0.2 :S.
When and are dependent random variables, after algebraic reduction, it became
In the case where and are independent, becomes
The linear correlation coefficient is . If this does not look familiar, the population correlation coefficient must be what you are looking for.
If the two random variables are independent, the coveriance =0. It follows that the population correlation coefficient must equal to zero. It cannot be anything but zero; however, it's not true for the linear regression coefficient of correlation.
For independent variable, the linear correlation need not be zero. 0.2 can be true.
I have a hunch that you are to find the linear correlation coefficient.