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Let X1, X2,..., Xn represent IID RVs with mean u and variance o?. Define RVs 0n as a function of X1, X2, ..., Xn: 1 On Xi n i=1 Question 1. What is the mean and variance of 0n? Question 2. Apply Chebyshev inequality to show that P [10, – µ? > 8²] < n82

Let X1, X2,..., Xn represent IID RVs with mean u and variance o?. Define RVs 0n as a function of X1, X2, ..., Xn: 1 On Xi n i=1 Question 1. What is the mean and variance of 0n? Question 2. Apply Chebyshev inequality to show that P [10, – µ? > 8²] < n82

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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Let X1, X2, ..., Xn represent IID RVs with mean u and variance o². Define RVs 0n as a function of X1, X2, ... , Xn: n 1 Xi i=1 Question 1. What is the mean and variance of 0,? Question 2. Apply Chebyshev inequality to show that P [18,, – µ² > 82] <2 n82 Note that as n → 0, RHS goes to zero and so does the LHS (WLLN). Therefore, for large n, 0n stays close to its mean with hihgh probability. This phenomenon is referred to as concentration of measure.
Transcribed Image Text:Let X1, X2, ..., Xn represent IID RVs with mean u and variance o². Define RVs 0n as a function of X1, X2, ... , Xn: n 1 Xi i=1 Question 1. What is the mean and variance of 0,? Question 2. Apply Chebyshev inequality to show that P [18,, – µ² > 82] <2 n82 Note that as n → 0, RHS goes to zero and so does the LHS (WLLN). Therefore, for large n, 0n stays close to its mean with hihgh probability. This phenomenon is referred to as concentration of measure.
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