The normal distribution is given as
N(x;a,b)=(1)/(\sqrt(2\pi b))e^(-((x-a)^(2))/(2b^(2)))
Calculate the expectation value
\mu =\int_(-\infty )^(\infty ) xN(x;a,b)dx
and the variance
\sigma ^(2)=\int_(-\infty )^(\infty ) (x-\mu )^(2)N(x;a,b)dx