I'd like to make an array of random samples from a Gaussian distrubution.
Mean value is 0 and variance is 1.
If I take enough samples, I would think my maximum value of a sample can be 0+1=1. However, I find that I get values like 4.2891 ...
My code:
x = 0+sqrt(1)*randn(100000,1);
mean(x)
var(x)
max(x)
This would give me a mean like 0, a var of 0.9937 but my maximum value is 4.2891?
Can anyone help me out why it does this?
As others have mentioned, there is no bound on the possible values that x can take on in a gaussian distribution. However, the farther x is from the mean, the less likely it is to be drawn.
To give you some intuition for what the variance actually means (for any distribution, not just the gaussian case), you can look at the 68-95-99.7 rule. The rule says:
sigma of the meansigma's of the meansigma's of the meanHere sigma = sqrt(var) is the standard deviation of the distribution.
So while in theory it is possible to draw any x from a gaussian distribution, in practice it is unlikely to draw anything past 5 or 6 standard deviations away for a population of 100000.
This will yield N random numbers using the gaussian normal distribution.
N = 100;
mu = 0;
sigma = 1;
Xs = normrnd(mu, sigma, N);
EDIT: I just realized that your code is in fact equivalent to what I've written. As others already pointed out: variance is not the maximum distance a sample can deviate from the mean! (It is just the average of the squares of those distances)
min(x). It would be nearly-max(x). Variance doesn' t mean the up/down bound. so "0 + 1 = 1" doesn' t make any sense in this case.