Question: The continuous random variable Y is said to have a lognormal distribution with parameters and if its probability density function, f(y), satisfies Show

The continuous random variable Y is said to have a lognormal distribution with parameters μ and σ if its probability density function, f(y), satisfies

1 (In y )* f(y) exp oyV27 (y > 0) 202 Show that X = ln (Y) has a normal distribution with mean μ and variance σ².

1 (In y )* f(y) exp oyV27 (y > 0) 202

Step by Step Solution

★★★★★

3.53 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To show that X lnY has a normal distribution with mean and variance 2 we need to find the mean and ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics For Engineering And The Sciences Questions!

A random variable Y is said to have a lognormal distribution if log Y has a normal distribution. Equivalently, we can write Y = e X , where X has a normal distribution. (a) If X 1 , X 2 , . . . is an...

A continuous random variable X is said to have a uniform distribution on the interval [a, b] if the PDF has the form (a) Find the probability that the value of A' is closer to a than it is to b. (b)...

A random variable X is said to have a beta distribution with parameters a and if and only if the density function of X is (a) Show that (b) Show that a. > 0; 0

A continuous random variable X is said to have an exponential distribution, written Exp(X), if its probability density function f is such that f(x)= xe-Az if z 20 0 if z 0 is a real...

solve them Consider the density function JKVI, 02, Y = 1); c) (C) PIX > Y);(d) F(X + Y = 4). A coin is flipped until 3 heads in succession occur. List only those elements of the sample space that...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

1. The heights of 10-year-old males are normally distributed with = 55.9 inches and s = 5.7inches. (a) Draw a normal curve with the parameters labeled. Shade the region that represents the proportion...

Kindly solve the question A continuous random variable X that can assume values between x = 1 and x = 3 has a density function given by f(x) = 1/2. (a) Show that the area under the curve is equal to...

solve these questions: The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint. 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.0 5.2 3.0 4.8 Assume...

30. Find the probability density function of Y = e x when X is normally distributed with parameters and 2 . The random variable Y is said to have a lognormal distribution (since log Y has a normal...

Can you use Twitter activity to forecast box office receipts on the opening weekend? The following data (stored in Twitter Movies) indicate the Twitter activity ("want to see") and the receipts ($)...

Mark was driving to school today with an initial velocity of 20 m/s in the positive x-direction, as shown in graph below. After 10 seconds Mark changes direction and accelerates at 3.5 m/s at 90 from...

What term is used to describes an approach in agile development that allows users to change their minds about what they want and need, and focuses on maximizing the development team's ability to...

9. Which of the following terms refers to disrespectful language? a. profanity b. jargon c. clichs d. colloquialisms

50. A department store sells sport shirts in three sizes (small, medium, and large), three patterns (plaid, print, and stripe), and two sleeve lengths (long and short). The accompanying tables give...

a. What is the probability that the next shirt sold is a medium, long-sleeved, print shirt?

b. What is the probability that the next shirt sold is a medium print shirt?

Morton Graphics successfully bid on .25 jobs printing standard notebook covers during the year using last year's price of $0.27 per cover. This amount was calculated from prior year costs, noting...

import java.util.*; import java.awt.*; import java.awt.event.*; import java.awt.image.*; import java.awt.geom.*; import java.io.*; import javax.imageio.*; // Main class public class ImageHistogram...

Assume that it is now January 1, 2015. Wayne-Martin Electric Inc. (WME) has developed a solar panel capable of generating 200% more electricity than any other solar panel currently on themarket. As a...