Help finding expected value of sum of random variables
I'm very much a Sage newbie, and I'm having trouble solving for the expected value of a discrete summation. I'll admit that I'm well removed from statistics, linear algebra, and econometrics, so it might be that what I'm trying to accomplish is illogical.
Consider the following parameters:
E ~ N(0,1) (i.e., E is a random variable distributed standard normal)
M ~ U(1,m) (i.e., M is a uniformly distributed random variable varying between 1 and m)
A = | Σ E×M | over the interval (1,N) (or the absolute value of the summation of E times M over interval 1,N)
I'd like to find the expected value of A as a function of N (or the limit of A as N goes to infinity, assuming A converges to a real number). Can I use Sage to solve for something like this (assuming it's solvable, which I think it is based on some simulation results)?