Calculating Variance of Y with X1, X2,...,X15

[ParisSpart]

The random variable X1, X2,...,X15 are independent and take each values ​​ +1,-1 with probability 1/2.

We define Y = sum from j=1 to 15(j*Xj)

whats is the variance VAR(Y)=?

i will find this with VAR(Y)=E(X^2)-(E(X)^2) but how i can find them?

 

[Mark44]

The random variable X1, X2,...,X15 are independent and take each values ​​ +1,-1 with probability 1/2.

We define Y = sum from j=1 to 15(j*Xj)

whats is the variance VAR(Y)=?

i will find this with VAR(Y)=E(X^2)-(E(X)^2) but how i can find them?

Your book probably has some theorems that cover finding the variance of a sum of multiple of random variables, such as the following.

If X and Y are random variables, and a and b are constants, then
1. Var(X + Y) = Var(X) + Var(Y) + 2Covar(X, Y)
2. Var(aX) = a²Var(X)