Generate random variables with specified 2nd moment ?

Hellow all,

I am using randn() to generate random variables. I know how to generate normal random variables with specific mean and variance. I am facing problem in generating these random variables with specific 2nd moment.

If random variables are:

x = randn(1,1000);

then 2nd moment is

momemt_2 = mean(x.^2);

Kindly help.

Answer 1

[Roger Wohlwend]

The second moment is the same as the variance of the random numbers!

>> x = randn(1,1000);
>> var(x)

ans =

      0.9193

>> mean(x.^2)

ans =

      0.9190

Your formula for the second moment assumes, however, that the mean of the time series x is zero.

[Furqan Haider]

I am sorry to accept your answer because its only applicable for random numbers with mean 'zero'. formula for variance is

variance = mean(x.^2) - (mean(x))^2;

whereas,

moment_2 = mean(x.^2);

Let me explain, in my case the mean is not zero.

Kindly help.

[Roger Wohlwend]

You use the wrong formula for the second moment. Consult the internet. The second moment is the variance. Your formula just implies a mean of zero. If the mean is not zero you have to adjust the formula.

moment_2 = mean((x - mean(x)).^2)