Normally distributed pseudorandom numbers using randn

Why doesn't

EDU>> r = 10.5 + 1.*randn(1,10);

EDU>> mean(r)

ans =

   10.5848

return a mean of 10.5 if I specified that this set of pseudorandom numbers should have a mean of 10.5 in the command line?

Answer 1

[Wayne King]

You cannot expect it to have exactly a mean of 10.5 in one realization of the random vector. If you repeat that experiment a large number of times, you will see the mean of the means will come very close to 10.5

    for nn = 1:1e4
      x = 10.5+randn(1,10);
      meanz(nn) = mean(x);
   end

    mean(meanz)

Just taking a sample from a N(mu,sigma^2) population does not guarantee the mean of the sample will be mu. You have to look at the sampling distribution of the sample mean.

[Joseph]

Ah, I see. Thanks a lot.

Joseph