# Interpreting Gaussian probabilities greater than 1 [duplicate]

Possible Duplicate:
Probability distribution value exceeding 1 is OK?

I'm a bit confused how I am getting probabilities greater than 1 when calculating p(x | mu, sigma) when x = mu. For example, if I run:

>> gaussProb(0, 0, 0.1)
ans =
1.2616


where gaussProb is a matlab function from the PMTK toolbox:

function p = gaussProb(X, mu, Sigma)
% Multivariate Gaussian distribution, pdf
% X(i,:) is i'th case
% *** In the univariate case, Sigma is the variance, not the standard
% deviation! ***

% This file is from pmtk3.googlecode.com

d = size(Sigma, 2);
X  = reshape(X, [], d);  % make sure X is n-by-d and not d-by-n
X = bsxfun(@minus, X, rowvec(mu));
logp = -0.5*sum((X/(Sigma)).*X, 2);
logZ = (d/2)*log(2*pi) + 0.5*logdet(Sigma);
logp = logp - logZ;
p = exp(logp);

end


Is this some fundamental property of the Gaussian distribution or an issue with numerical accuracy in the computation?

I've come across this issue by trying to weight samples from a Gaussian distribution obtained from a Gaussian process prediction, where I will get massive probabilities.

Thanks

The code in the question returns the values of probability density function. The values of probability density function can be greater than one. The actual probability $P(X<x)$ for random variable $X$ with probability density function $p(x)$ is integral $\int_{-\infty}^xp(t)dt$. The values of this integral are of course restricted to interval $[0,1]$.