Can you help me with something? I get stuck everytime i try to solve the following problem.

Let Xi, 1<=i<=10 be independent random variables such that EXi = 10 and Var Xi = 6. Let

Calculate Var Y.

I tried to solve it using the fact that Var Y = Cov(Y,Y). That leads to:

The second term can be decomposed in two types:The second type is zero because the variables are independent. The first type can be calculated:

Ok. But here's the problem: look what i get when I calculate Cov(XiXi+1,XiXi+1):

And I can't get rid of this E(X_{i+1)^2)!

I appreciate any help. Thanks