$X=[x_1, x_2,...x_n] Y = [y_1, y_2,...y_n]$
If $x_i, y_i$ are both random variables with
$P(x=1) = .5$
$ P(x=2) = .5 $
How would I find the expected value of the inner product of both of these random vectors?$E[X.Y]$
I'm thrown off with this problem, as I don't know how exactly to work with random vectors or if any additional rules apply when finding the expected value.
My gut feeling is
$E[X.Y] = [E[x_1y_1], E[x_2y_2],.....,E[x_ny_n]]$
Is this the right approach?