Generate random variables with specified 2nd moment ?

2014 6 11
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更新时间：2014 6 11
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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.

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回答（1 个）

Roger Wohlwend
Roger Wohlwend 2014-6-11

0 个投票

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.

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Furqan Haider
Furqan Haider 2014-6-11
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
Roger Wohlwend 2014-6-11
编辑：Roger Wohlwend 2014-6-11
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)

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