Question

Random variable x has standard normal distribution.

Give the value for the smallest x where the second derivative of the distribution function is zero

Answer 1

Here as it is given Random variable x has standard normal distribution.

f(x) =

now if we assume

= c then

f(x) = c

now taking first derivativ

f'(x) = c [-x ]

f''(x) = c d/dx [-x ]

f"(x) = c [x² - ]

f"(x) = c (x² -1)

now it is asked that the second derivative of the distribution function is zero

f"(x) = 0  

c (x² -1) = 0

x² -1 = 0

x = -1 and 1

so here the smallest x where the second derivative of the distribution function is zero is (-1).