hi thanks here is my work i have showed that equality hold for the first moment but i'm not sure for the rest

x~N(mu,sigma^2)

Z= x-mu/sigma ~ N(0,1)

E[Z]

we have pdf of normal distribution

1/(2*pi)^1/2 * exp(-1/2*x^2)

we have to show that

E(Z) ~ N(0,1)

integral (z*1/(2*pi)*1/2 *exp(-1/2*z^2) dx =

= -1/2*pi*1/2 *exp(-1/2*z^2) = 0

thanks

sorry i dont know how to type in lytex form