The monthly salary of women that are in the labor force in a large town, Y, follows a gamma distribution with expected value 500 and variance 125. The city is planning to obtain a random sample of 100 women to obtain some information. The city is planning to ask the 100 women about their salary. O What is the probability that the average salary of the 100 women in the sample is larger than 1,500? (i) If, in this town, 20% of the women have a monthly salary larger than 3,000, what is the probability that in the random sample of 100 women more than 20% of them make a salary larger than 3,000? Show work. (ii) Would W = (4/100) E, yi be an unbiased estimator of the average salary of the women in the large town? (Note: "unbiased" means that the expected value of W equals the mean of the population of women,.) (iv) What is the joint distribution of the 100 random variables with the same density function as in this problem?

The monthly salary of women that are in the labor force in a large town, Y, follows a gamma distribution with expected value 500 and variance 125. The city is planning to obtain a random sample of 100 women to obtain some information. The city is planning to ask the 100 women about their salary. O What is the probability that the average salary of the 100 women in the sample is larger than 1,500? (i) If, in this town, 20% of the women have a monthly salary larger than 3,000, what is the probability that in the random sample of 100 women more than 20% of them make a salary larger than 3,000? Show work. (ii) Would W = (4/100) E, yi be an unbiased estimator of the average salary of the women in the large town? (Note: "unbiased" means that the expected value of W equals the mean of the population of women,.) (iv) What is the joint distribution of the 100 random variables with the same density function as in this problem?

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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Question

The monthly salary of women that are in the labor force in a large town, Y, follows a gamma distribution with expected value 500 and variance 125. The
city is planning to obtain a random sample of 100 women to obtain some information. The city is planning to ask the 100 women about their salary.
(i)
What is the probability that the average salary of the 100 women in the sample is larger than 1,500?
(ii)
If, in this town, 20% of the women have a monthly salary larger than 3,000, what is the probability that in the random sample of 100 women more
than 20% of them make a salary larger than 3,000? Show work.
(iii) Would W = (4/100) E, Y; be an unbiased estimator of the average salary of the women in the large town? (Note: "unbiased" means that the
expected value of W equals the mean of the population of women.)
(iv) What is the joint distribution of the 100 random variables with the same density function as in this problem?

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