[3] Consider the model of aggregating private signals. suppose that we model the private information (or expectation) of agent i, denoted by xi, as the sum of the fundamental (0) and a margin of error (e₁): x₁ = 0+ €₁ In words, we model agent i as if it can observe the fundamental value with some noise (which we call the margin of error). Notice that the agent only observes Xi but can not tell what part of it is and what part is ei, otherwise, agent i would know perfectly. But this point is not very important because in the model, agent i doesn't really do anything with their signal. The only thing that they do is to pass on their signal to the person, say a public authority, who collects all of the private signals. So in this model, we are interested in what kind of information this public authority can learn based on the signals received. In particular, we consider the public authority receives all of these private signals (or expectations) x1,x2,..., n from n individuals (or respondents if we are talking about a survey of expectations) and our interest is For each of the following cases, suppose that have access to 140 independent private signals xi. a) Suppose that the margin of errors, eis, are independent and coming from a normal distribution with mean 0 and variance 25. What is the distribution of 0? b) Suppose that the margin of errors, eis, are coming from the following distri- bution e -2 -1 0 1 2 P(e) 0.1 0.1 0.2 0.3 0.4 What would be the best estimator for 0? (It is an expression involving X and E(e)). What is the distribution of 0? c) Suppose that the margin of errors, eis, are independent and coming from an exponential distribution with mean 1.5. What would be the best estimator for 0? What is the distribution of 0?
[3] Consider the model of aggregating private signals. suppose that we model the private information (or expectation) of agent i, denoted by xi, as the sum of the fundamental (0) and a margin of error (e₁): x₁ = 0+ €₁ In words, we model agent i as if it can observe the fundamental value with some noise (which we call the margin of error). Notice that the agent only observes Xi but can not tell what part of it is and what part is ei, otherwise, agent i would know perfectly. But this point is not very important because in the model, agent i doesn't really do anything with their signal. The only thing that they do is to pass on their signal to the person, say a public authority, who collects all of the private signals. So in this model, we are interested in what kind of information this public authority can learn based on the signals received. In particular, we consider the public authority receives all of these private signals (or expectations) x1,x2,..., n from n individuals (or respondents if we are talking about a survey of expectations) and our interest is For each of the following cases, suppose that have access to 140 independent private signals xi. a) Suppose that the margin of errors, eis, are independent and coming from a normal distribution with mean 0 and variance 25. What is the distribution of 0? b) Suppose that the margin of errors, eis, are coming from the following distri- bution e -2 -1 0 1 2 P(e) 0.1 0.1 0.2 0.3 0.4 What would be the best estimator for 0? (It is an expression involving X and E(e)). What is the distribution of 0? c) Suppose that the margin of errors, eis, are independent and coming from an exponential distribution with mean 1.5. What would be the best estimator for 0? What is the distribution of 0?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Show full answers and steps to part a) b) & c) to exercise 3 below. Please don’t use R or excel when solving this exercise
![[3] Consider the model of aggregating private signals.
suppose
that we model the private information (or expectation) of agent i, denoted by x₁,
as the sum of the fundamental (0) and a margin of error (e;):
x₁ = 0 + ei
In words, we model agent i as if it can observe the fundamental value with some
noise (which we call the margin of error). Notice that the agent only observes xi
but can not tell what part of it is and what part is ei, otherwise, agent i would
know perfectly. But this point is not very important because in the model, agent
i doesn't really do anything with their signal. The only thing that they do is to
pass on their signal to the person, say a public authority, who collects all of the
private signals. So in this model, we are interested in what kind of information
this public authority can learn based on the signals received. In particular, we
consider the public authority receives all of these private signals (or expectations)
x1, x2,..., n from n individuals (or respondents if we are talking about a survey
of expectations) and our interest is
For each of the following cases, suppose that have access to 140 independent private
signals xi.
a) Suppose that the margin of errors, eis, are independent and coming from a
normal distribution with mean 0 and variance 25. What is the distribution
of 0?
b) Suppose that the margin of errors, es, are coming from the following distri-
bution
e
P(e)
-2 -1 0 1 2
0.1 0.1
0.2 0.3 0.4
What would be the best estimator for ? (It is an expression involving X and
E(e)). What is the distribution of 0?
c) Suppose that the margin of errors, eis, are independent and coming from an
exponential distribution with mean 1.5. What would be the best estimator
for 0? What is the distribution of 0?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2F20e32cf1-c963-4d72-97dc-806d328fcde7%2Fefx5qse_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[3] Consider the model of aggregating private signals.
suppose
that we model the private information (or expectation) of agent i, denoted by x₁,
as the sum of the fundamental (0) and a margin of error (e;):
x₁ = 0 + ei
In words, we model agent i as if it can observe the fundamental value with some
noise (which we call the margin of error). Notice that the agent only observes xi
but can not tell what part of it is and what part is ei, otherwise, agent i would
know perfectly. But this point is not very important because in the model, agent
i doesn't really do anything with their signal. The only thing that they do is to
pass on their signal to the person, say a public authority, who collects all of the
private signals. So in this model, we are interested in what kind of information
this public authority can learn based on the signals received. In particular, we
consider the public authority receives all of these private signals (or expectations)
x1, x2,..., n from n individuals (or respondents if we are talking about a survey
of expectations) and our interest is
For each of the following cases, suppose that have access to 140 independent private
signals xi.
a) Suppose that the margin of errors, eis, are independent and coming from a
normal distribution with mean 0 and variance 25. What is the distribution
of 0?
b) Suppose that the margin of errors, es, are coming from the following distri-
bution
e
P(e)
-2 -1 0 1 2
0.1 0.1
0.2 0.3 0.4
What would be the best estimator for ? (It is an expression involving X and
E(e)). What is the distribution of 0?
c) Suppose that the margin of errors, eis, are independent and coming from an
exponential distribution with mean 1.5. What would be the best estimator
for 0? What is the distribution of 0?
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