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3.1 Let Y~ normal (uy;o) and X = e, i.e. Y = logeX, then we say that X is distributed lognormal (uy;o); the coefficient of variation is vx. Show that μ₁ (X) = μ (v¹² +6v +15v +16v +3v) where μ4(X) is the 4th central moment about ux. 3.2 Suppose X follows a lognormal distribution with parameters uy=1 and oy = 1. Determine Hx and ox. 3.3 Let X₁ = 1.25X. Is X, distributed lognormal? (Hint: Use cumulative distribution function to show). 3.4 Determine the probability that X, exceed 1. (Use information above). 3.5 Determine the 80th percentile of X₁. (Use information above).

3.1 Let Y~ normal (uy;o) and X = e, i.e. Y = logeX, then we say that X is distributed lognormal (uy;o); the coefficient of variation is vx. Show that μ₁ (X) = μ (v¹² +6v +15v +16v +3v) where μ4(X) is the 4th central moment about ux. 3.2 Suppose X follows a lognormal distribution with parameters uy=1 and oy = 1. Determine Hx and ox. 3.3 Let X₁ = 1.25X. Is X, distributed lognormal? (Hint: Use cumulative distribution function to show). 3.4 Determine the probability that X, exceed 1. (Use information above). 3.5 Determine the 80th percentile of X₁. (Use information above).

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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3.1 Let Y~ normal (uy;o) and X = e, i.e. Y=logeX, then we say that X is distributed lognormal (uy;o); the coefficient of variation is vx. Show that 4 H₁ (X) = μ (v¹² +6v X X about µx. 3.2 Suppose X follows a lognormal distribution with parameters µç= 1 and o、=1. and ox. Determine µx 3.3 Let X₁ = +15v +16vg +3v) where 14(X) is the 4th central moment X to show). 1.25X. Is X, distributed lognormal? (Hint: Use cumulative distribution function 3.4 Determine the probability that X₁ exceed 1. (Use information above). 3.5 Determine the 80th percentile of X₁. (Use information above).
Transcribed Image Text:3.1 Let Y~ normal (uy;o) and X = e, i.e. Y=logeX, then we say that X is distributed lognormal (uy;o); the coefficient of variation is vx. Show that 4 H₁ (X) = μ (v¹² +6v X X about µx. 3.2 Suppose X follows a lognormal distribution with parameters µç= 1 and o、=1. and ox. Determine µx 3.3 Let X₁ = +15v +16vg +3v) where 14(X) is the 4th central moment X to show). 1.25X. Is X, distributed lognormal? (Hint: Use cumulative distribution function 3.4 Determine the probability that X₁ exceed 1. (Use information above). 3.5 Determine the 80th percentile of X₁. (Use information above).
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