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)
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ISBN:9780134753119
Author:Sheldon Ross
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79d4e09e-81af-4658-b2db-40904eb93eef%2F8059bba4-00f8-40e1-b715-2263393e9a42%2Fxfghhg7_processed.jpeg&w=3840&q=75)
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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