Provide an appropriate response.The standard normal probability density function is defined by f(x) = e- x2/2. (a) Use the fact that dx = 1 to show that dx =.(b) Use the result in part (a) to show that the standard normal probability density function has variance 1.

Question

What will be an ideal response?

Answer 1

(a) Since dx = 1 and f(x) is an even function,  dx = . Then dx = dx =   =  dx =  .  
(b) The variance of the distribution is equal to dx = dx + dx =  +  = 1.