Calculate some weird RV's variance
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