[5] Consider the private information model collects private signals. This is the model we covered in class. As we did in class, suppose that we model the private information of agent i, denoted by xi, as the sum of the fundamental (0) and a margin of error (ei): x₂ = 0 + ei Furthermore, suppose that the margin of errors, ei's, are coming from the following distribution e -2 -1 0 1 2 P(e) 0.1 0.1 0.2 0.3 0.3 a) What would be the best estimator for 0? Explain your answer.

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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[5] Consider the private information model where there is a public authority that
collects private signals. This is the model we covered in class. As we did in class,
suppose that we model the private information of agent i, denoted by xi, as the
sum of the fundamental (0) and a margin of error (ei):
xi=0tei
Furthermore, suppose that the margin of errors, e;'s, are coming from the following
distribution
2
e
-2 -1 0 1
P(e) 0.1 0.1 0.2 0.3 0.3
a) What would be the best estimator for 0? Explain your answer.
b) What is the distribution of X?
c) What is the probability that the best estimator will deviate from by more
than 0.7? For this case, just describe how you would find this probability.
Transcribed Image Text:[5] Consider the private information model where there is a public authority that collects private signals. This is the model we covered in class. As we did in class, suppose that we model the private information of agent i, denoted by xi, as the sum of the fundamental (0) and a margin of error (ei): xi=0tei Furthermore, suppose that the margin of errors, e;'s, are coming from the following distribution 2 e -2 -1 0 1 P(e) 0.1 0.1 0.2 0.3 0.3 a) What would be the best estimator for 0? Explain your answer. b) What is the distribution of X? c) What is the probability that the best estimator will deviate from by more than 0.7? For this case, just describe how you would find this probability.
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