Homework Help is Here – Start Your Trial Now!
Math
Statistics
Problem 4 (counts as two problems): Let X1, X2, ... , X,be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The following set of steps illustrates the Law of Large Numbers at work. a) Compute the mean and the variance of X1 (which is the same for X2, X3, etc.) b) Use your answer to (a) to compute the mean and variance of p = (X1 + X2 + .+ X„), which is the proportion of "ones" observed in the n instances of X;. c) Suppose n= 10,000. Use Chebyshev's inequality to provide an upper bound for the probability that the difference between p and p exceeds 0.05. d) Use calculus to show that if p is a number between 0 and 1, then p(1 – p) < e) Use your answers to (c) and (d) to provide an upper bound, that does not depend on p, for the probability that the difference between p and p exceeds 0.05. f) Interpret this problem in the context of randomly sampling 10,000 people from a large population, asking them a yes-no question, and using the result to make an inference about the whole population. %3D

Problem 4 (counts as two problems): Let X1, X2, ... , X,be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The following set of steps illustrates the Law of Large Numbers at work. a) Compute the mean and the variance of X1 (which is the same for X2, X3, etc.) b) Use your answer to (a) to compute the mean and variance of p = (X1 + X2 + .+ X„), which is the proportion of "ones" observed in the n instances of X;. c) Suppose n= 10,000. Use Chebyshev's inequality to provide an upper bound for the probability that the difference between p and p exceeds 0.05. d) Use calculus to show that if p is a number between 0 and 1, then p(1 – p) < e) Use your answers to (c) and (d) to provide an upper bound, that does not depend on p, for the probability that the difference between p and p exceeds 0.05. f) Interpret this problem in the context of randomly sampling 10,000 people from a large population, asking them a yes-no question, and using the result to make an inference about the whole population. %3D

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
Problem 4 (counts as two problems): Let X1, X2, ... , X,be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The following set of steps illustrates the Law of Large Numbers at work. a) Compute the mean and the variance of X1 (which is the same for X2, X3, etc.) b) Use your answer to (a) to compute the mean and variance of p = (X1 + X2 + .+ X„), which is the proportion of "ones" observed in the n instances of X;. c) Suppose n= 10,000. Use Chebyshev's inequality to provide an upper bound for the probability that the difference between p and p exceeds 0.05. d) Use calculus to show that if p is a number between 0 and 1, then p(1 – p) < e) Use your answers to (c) and (d) to provide an upper bound, that does not depend on p, for the probability that the difference between p and p exceeds 0.05. f) Interpret this problem in the context of randomly sampling 10,000 people from a large population, asking them a yes-no question, and using the result to make an inference about the whole population. %3D
Transcribed Image Text:Problem 4 (counts as two problems): Let X1, X2, ... , X,be a collection of independent discrete random variables that all take the value 1 with probability p and take the value 0 with probability (1-p). The following set of steps illustrates the Law of Large Numbers at work. a) Compute the mean and the variance of X1 (which is the same for X2, X3, etc.) b) Use your answer to (a) to compute the mean and variance of p = (X1 + X2 + .+ X„), which is the proportion of "ones" observed in the n instances of X;. c) Suppose n= 10,000. Use Chebyshev's inequality to provide an upper bound for the probability that the difference between p and p exceeds 0.05. d) Use calculus to show that if p is a number between 0 and 1, then p(1 – p) < e) Use your answers to (c) and (d) to provide an upper bound, that does not depend on p, for the probability that the difference between p and p exceeds 0.05. f) Interpret this problem in the context of randomly sampling 10,000 people from a large population, asking them a yes-no question, and using the result to make an inference about the whole population. %3D
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS