Help finding expected value of sum of random variables

asked 2016-03-08 11:45:16 -0600

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)?

edit retag flag offensive close merge delete

Comments

What does your summation mean in the definition of A? It is mathematically unclear to me.

vdelecroix gravatar imagevdelecroix ( 2016-03-09 09:22:31 -0600 )edit