Re: [Axiom-mail] integrate the PDF of normal distribution

[ming lu]

It works:) .
Thanks,
Ming

On 10/24/06, Themos Tsikas <address@hidden> wrote:
> (1) -> sigma:=(theta^2)
>
>             2
>   (1)  theta
>                                                     Type: Polynomial Integer
> (2) -> f:= x/(sigma*sqrt(2*%pi))*exp(-(x-mu)**2/(2*sigma**2))
>
>               2             2
>            - x  + 2mu x - mu
>            ------------------
>                        4
>                  2theta
>        x %e
>   (2)  ----------------------
>                  2 +----+
>             theta \|2%pi
>                                                     Type: Expression Integer
> (3) -> result:EXPR INT:=integrate(f,x=%minusInfinity..%plusInfinity)
>
>             +---+
>         2mu\|%pi
>   (3)  -----------
>         +-+ +----+
>        \|2 \|2%pi
>                                                     Type: Expression Integer
>
> -- to simplify one way
> (4) -> tower:= tower result
>
>                 +-+  +---+  +----+
>   (4)  [mu,%pi,\|2 ,\|%pi ,\|2%pi ]
>                                         Type: List Kernel Expression Integer
> (5) -> eval(result,[tower.5 =((tower.3)::EXPR INT )*((tower.4)::EXPR INT)])
>
>   (5)  mu
>                                                     Type: Expression Integer
> -- to simplify another way
> (6) -> simplify1:= rule sqrt(2*%pi) == sqrt(2)*sqrt(%pi)
>
>          +----+     +-+ +---+
>   (6)  \|2%pi  == \|2 \|%pi
>                        Type: RewriteRule(Integer,Integer,Expression Integer)
> (7) -> simplify1  result
>
>   (7)  mu
>                                                     Type: Expression Integer
>
>
>
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