Let x ~ n(0, 1) and y = ex. y is called a log-normal random variable.
(a) find the probability density function of y .
(b) find the nth moment e(yn) of y .
hint. do not compute the moment generating function of y . instead relate
the nth moment of y to an expectation of x that you know.

If is the cumulative distribution function for , then

Then the probability density function for is :

The th moment of is

Let , so that and :

Complete the square in the exponent:

But is exactly the PDF of a normal distribution with mean and variance 1; in other words, the 0th moment of a random variable :

so we end up with

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length

what's the question?

step-by-step explanation:

there is no question.