ABSTRACT
The probability density function of a normal random variable X with mean µ and standard deviation σ is given by
f(x|µ, σ) = 1 σ √ 2π
exp
[ − (x− µ)
2σ2
] ,−∞ < x <∞, −∞ < µ <∞, σ > 0.
This distribution is commonly denoted by N(µ, σ2). The cumulative distribution function (cdf) is given by
F (x|µ, σ) = ∫ x −∞
f(t|µ, σ)dt.