Choose the best answer, and explain. If X is a random

Chapter 4, Problem 8E

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QUESTION:

Choose the best answer, and explain. If X is a random variable with a lognormal distribution, then _________

i. the mean of X is always greater than the median.

ii. the mean of X is always less than the median.

iii. the mean may be greater than, less than, or equal to the median, depending on the value of \(\sigma).

Equation transcription:

Text transcription:

\sigma

Questions & Answers

QUESTION:

Choose the best answer, and explain. If X is a random variable with a lognormal distribution, then _________

i. the mean of X is always greater than the median.

ii. the mean of X is always less than the median.

iii. the mean may be greater than, less than, or equal to the median, depending on the value of \(\sigma).

Equation transcription:

Text transcription:

\sigma

ANSWER:

Solution 8E

Step1 of 2:

Let us consider a random variable X it follows log normal distribution with mean and variance

That is

Here our goal is:

i).We need to check whether the mean of X is always greater than the median.

ii).We need to check whether the mean of X is always less than the median.

iii).

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