Solution Found!
Let the distribution of X be N(?, ?2). Show that the
Chapter 3, Problem 8E(choose chapter or problem)
QUESTION:
Let the distribution of X be \(N(\mu, \sigma^2)\). Show that the points of inflection of the graph of the pdf of X occur at \(x = \mu \pm \sigma\).
Questions & Answers
QUESTION:
Let the distribution of X be \(N(\mu, \sigma^2)\). Show that the points of inflection of the graph of the pdf of X occur at \(x = \mu \pm \sigma\).
ANSWER:Answer :
Step 1 of 2 :
A random variable X is normally distributed with mean and standard deviation
.
The probability density function is
f(x) = .
The claim is to show that the point of the graph of the pdf of X occur at x = +
The first derivative of the f(x) is
=
=