Simulation Lecture Notes

Lecture Notes for Simulation

IID samples from the random variable X with the underlying n-sample-mean population have the form

X = (Y₁ + Y₂ + ... + Y_n)/n

where Y_i is a random variable from the original population (server utilization in the example). The variance of X (that is, v_n²) is

Var[X] = Var[(Y₁ + Y₂ + ... + Y_n)/n]

1/n is a constant and can brought outside the variance.

Var[X] = (Var[Y₁ + Y₂ + ... + Y_n])/n²

The variance distributes over addition under the assumption of independent samples.

Var[X] = (Var[Y₁] + Var[Y₂] + ... + Var[Y_n])/n²

By assumption, the variance of the original population is v², so Var[Y_i] = v² for 1 <= i <= n.

This page last modified on 2 March 2005.