Lecture Notes for Simulation

23 March 2005 - Output Analysis

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

X = (Y1 + Y2 + ... + Yn)/n

where Yi is a random variable from the original population (server utilization in the example). The expected value of X (that is, the mean mn) is

E[X] = E[(Y1 + Y2 + ... + Yn)/n]

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

E[X] = (E[Y1 + Y2 + ... + Yn])/n

Expectation distributes over addition.

E[X] = (E[Y1] + E[Y2] + ... + E[Yn])/n

By hypothesis, the expected value of the original population is m, so E[Yi] = m for 1 <= i <= n.

E[X]=(m + m + ... + m)/n
=(nm)/n
=m

This page last modified on 2 March 2005.