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r.v. with the following probability distribution Let Y be a P(Y= 0) = 0.22 and P(Y = 1) = 0.78 we developed the sampling distribution of sample means (Y) for n = 2 and n = 5. In this exercise, we are going to develop sampling distributions of sample medians and sample maximums. a) Suppose we take three draws from this distribution, Y₁, Y₂ and Y3, and then compute sample median (denoted by M) and sample maximum (denoted by X). What are the sampling distributions of M and X? Also, represent their distributions on a bar chart. b) Repeat the same exercise in the previous part for n = 5. c) In each case, compute the expected value and the variance of M and X. How do they compare to the population distribution Y? Does anything change as the sample size increases?

r.v. with the following probability distribution Let Y be a P(Y= 0) = 0.22 and P(Y = 1) = 0.78 we developed the sampling distribution of sample means (Y) for n = 2 and n = 5. In this exercise, we are going to develop sampling distributions of sample medians and sample maximums. a) Suppose we take three draws from this distribution, Y₁, Y₂ and Y3, and then compute sample median (denoted by M) and sample maximum (denoted by X). What are the sampling distributions of M and X? Also, represent their distributions on a bar chart. b) Repeat the same exercise in the previous part for n = 5. c) In each case, compute the expected value and the variance of M and X. How do they compare to the population distribution Y? Does anything change as the sample size increases?

A First Course in Probability (10th Edition)
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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r.v. with the following probability distribution Let y be a P(Y=0)= 0.22 and P(Y= 1) = 0.78 we developed the sampling distribution of sample means (Y) for n = 2 and n=5. In this exercise, we are going to develop sampling distributions of sample medians and sample maximums. a) Suppose we take three draws from this distribution, Y₁, Y₂ and Y3, and then compute sample median (denoted by M) and sample maximum (denoted by X). What are the sampling distributions of M and X? Also, represent their distributions on a bar chart. b) Repeat the same exercise in the previous part for n = 5. c) In each case, compute the expected value and the variance of M and X. How do they compare to the population distribution Y? Does anything change as the sample size increases?
Transcribed Image Text:r.v. with the following probability distribution Let y be a P(Y=0)= 0.22 and P(Y= 1) = 0.78 we developed the sampling distribution of sample means (Y) for n = 2 and n=5. In this exercise, we are going to develop sampling distributions of sample medians and sample maximums. a) Suppose we take three draws from this distribution, Y₁, Y₂ and Y3, and then compute sample median (denoted by M) and sample maximum (denoted by X). What are the sampling distributions of M and X? Also, represent their distributions on a bar chart. b) Repeat the same exercise in the previous part for n = 5. c) In each case, compute the expected value and the variance of M and X. How do they compare to the population distribution Y? Does anything change as the sample size increases?
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