4. The continuous random variable X has a lognormal distribution if the random variable Y = In(X) has a normal distribution with mean and variance o². Let X₁...., X20 be a random sample from a lognormal distribution with unknown parameters and o². If the sample values are: 5.75 5.73 5.57 5.86 5.28 5.26 (a) (b) 5.67 5.42 6.02 5.85 5.39 5.50 5.37 5.34 5.66 6.13 5.79 6.04 6.07 5.64 What is the value of the unbiased estimate of ? What is the value of the maximum likelihood estimate of μ? (c) What is the value of the unbiased estimate of o²? (d) What is the value of the maximum likelihood estimate of o²?
4. The continuous random variable X has a lognormal distribution if the random variable Y = In(X) has a normal distribution with mean and variance o². Let X₁...., X20 be a random sample from a lognormal distribution with unknown parameters and o². If the sample values are: 5.75 5.73 5.57 5.86 5.28 5.26 (a) (b) 5.67 5.42 6.02 5.85 5.39 5.50 5.37 5.34 5.66 6.13 5.79 6.04 6.07 5.64 What is the value of the unbiased estimate of ? What is the value of the maximum likelihood estimate of μ? (c) What is the value of the unbiased estimate of o²? (d) What is the value of the maximum likelihood estimate of o²?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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