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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?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 43CR
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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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