The normal probability function is usually depicted:
Y = { 1/[ σ * sqrt(2π) ] } * e-(x - μ)2/2σ2
Is there an algebraic expression for the distribution function (algebraic anti-derivative) for the above equation or does one have to always have a numeric (use of tables) solution?

Question

The normal probability function is usually depicted:
Y = { 1/[ σ * sqrt(2π) ] } * e-(x - μ)2/2σ2
Is there an algebraic expression for the distribution function (algebraic anti-derivative) for the above equation or does one have to always have a numeric (use of tables) solution?

anonymous · Answer

there is no cumulative distribution function expressible in terms of elementary functions, unfortunately. http://en.wikipedia.org/wiki/Error_function