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et Z ~ N(0,1). If we define X = eºz+, then we say that X has a log-normal distribution with parameters μl and o, and we write X~ LogNormal(μ, o). a. If X~ LogNormal(μ, o), find the CDF of X in terms of the function. b. Find EX and Var(X).

et Z ~ N(0,1). If we define X = eºz+, then we say that X has a log-normal distribution with parameters μl and o, and we write X~ LogNormal(μ, o). a. If X~ LogNormal(μ, o), find the CDF of X in terms of the function. b. Find EX and Var(X).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Problem 22** Let \( Z \sim N(0,1) \). If we define \( X = e^{\sigma Z + \mu} \), then we say that \( X \) has a log-normal distribution with parameters \(\mu\) and \(\sigma\), and we write \( X \sim LogNormal(\mu, \sigma) \). a. If \( X \sim LogNormal(\mu, \sigma) \), find the CDF of \( X \) in terms of the \(\Phi\) function. b. Find \( E(X) \) and \( Var(X) \).
Transcribed Image Text:**Problem 22** Let \( Z \sim N(0,1) \). If we define \( X = e^{\sigma Z + \mu} \), then we say that \( X \) has a log-normal distribution with parameters \(\mu\) and \(\sigma\), and we write \( X \sim LogNormal(\mu, \sigma) \). a. If \( X \sim LogNormal(\mu, \sigma) \), find the CDF of \( X \) in terms of the \(\Phi\) function. b. Find \( E(X) \) and \( Var(X) \).
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