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Normal Distribution   The normal pdf is   The normal
distribution is a two-parameter family of curves. The first
parameter, µ, is the mean. The second, σ, is the standard
deviation. The standard normal distribution (written Φ(x)) sets
µ to 0 and σ to 1.  Φ(x) is functionally related to the error
function, erf.  The first use of the normal distribution was as
a continuous approximation to the binomial.  The usual
justification for using the normal distribution for modeling is
the Central Limit Theorem, which states (roughly) that the sum
of independent samples from any distribution with finite mean
and variance converges to the normal distribution as the sample
size goes to infinity.   To use statistical parameters such as
mean and standard deviation reliably, you need to have a good
estimator for them. The maximum likelihood estimates (MLEs)
provide one such estimator. However, an MLE might be biased,
which means that its expected value of the par