Provide an appropriate response.The standard normal probability density function is defined by f(x) = e- x2/2. (a) Show that dx = .(b) Use the result in part (a) to show that the standard normal probability density function has mean 0.

Question

What will be an ideal response?

Answer 1

(a) dx =  dx =  = .
(b) Since y =  x e^{- x2/2} is an odd function,  dx = - dx = - . The mean of the distribution is equal to  dx = dx + dx = -  +  = 0.