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

[Themos Tsikas]

(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