Normal probability density function
Y = normpdf(X,mu,sigma)
Y = normpdf(X)
Y = normpdf(X,mu)
Y = normpdf(X,mu,sigma) computes the pdf at each of the values in X using the normal distribution with mean mu and standard deviation sigma. X, mu, and sigma can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs. The parameters in sigma must be positive.
The normal pdf is
The likelihood function is the pdf viewed as a function of the parameters. Maximum likelihood estimators (MLEs) are the values of the parameters that maximize the likelihood function for a fixed value of x.
The standard normal distribution has µ = 0 and σ = 1.
If x is standard normal, then xσ + µ is also normal with mean µ and standard deviation σ. Conversely, if y is normal with mean µ and standard deviation σ, then x = (y – µ) / σ is standard normal.
Y = normpdf(X) uses the standard normal distribution (mu = 0, sigma = 1).
Y = normpdf(X,mu) uses the normal distribution with unit standard deviation (sigma = 1).