Forums

zero mean random variables

Started by mohan prasad March 4, 2003
Hi,
Am trying to generate complex gaussian random
variables using the randn function but when I
calculated the mean of those random variables it is
not giving zero as answer.Can anyone tell why this is
happening?
mohan



Message
Let's say you are taking multiple independent identically distributed values from a gaussian random value generator.  The mean of those values is itself a random variable.  Say you take values X1, X2, ..., XN from a random number generator, then the mean of them is MX = sum(X1,...,XN)/N, which itself is a random variable.  The expectation of MX (or its mean, if you formed many MX's from different sets of Xi's, i from 1 to N) is zero, but the variance of MX, E{ MX^2 } if MX is zero-mean, is NOT zero.
 
If the variance of the random value generator was 1, then the variance of MX is 1/N.  So any finite set of X's has a mean that on average will be zero, but is not guaranteed (indeed, has infinitesimal probability of being exactly) zero.  The larger the set, the closer MX should be to zero.
 
Most likely, the number generator is working perfectly, and you are observing an effect caused by a finite set of samples.
 
Sincerely,
Glen Ragan
 
----Original Message-----
From: mohan prasad [mailto:m...@yahoo.com]
Sent: Tuesday, March 04, 2003 1:48 PM
To: m...@yahoogroups.com
Subject: [matlab] zero mean random variables

Hi,
Am trying to generate complex gaussian random
variables using the randn function but when I
calculated the mean of those random variables it is
not giving zero as answer.Can anyone tell why this is
happening?
mohan


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