3. [Hierarchical models] Some economic model assumes that individuals are heterogeneous in their productivity factor. This factor can range between 0 and 1, and is uniformly distributed across the economy. Thus, the productivity factor of a randomly selected individual is modeled with the uniform random variable, X ~ U[0, 1]. An output produced by an individual is random, but depends on the productivity, Y|X ~ B(n, X), where n is some natural number. 1 (a) Using the Law of Total Expectations find E(Y). (b) Using the Law of Total Variances, find V(Y).
3. [Hierarchical models] Some economic model assumes that individuals are heterogeneous in their productivity factor. This factor can range between 0 and 1, and is uniformly distributed across the economy. Thus, the productivity factor of a randomly selected individual is modeled with the uniform random variable, X ~ U[0, 1]. An output produced by an individual is random, but depends on the productivity, Y|X ~ B(n, X), where n is some natural number. 1 (a) Using the Law of Total Expectations find E(Y). (b) Using the Law of Total Variances, find V(Y).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![3. [Hierarchical models] Some economic model assumes that individuals are heterogeneous in their
productivity factor. This factor can range between 0 and 1, and is uniformly distributed across the
economy. Thus, the productivity factor of a randomly selected individual is modeled with the uniform
random variable, X ~ U[0, 1]. An output produced by an individual is random, but depends on the
productivity, Y|X ~ B(n, X), where n is some natural number.
1
(a) Using the Law of Total Expectations find E(Y).
(b) Using the Law of Total Variances, find V(Y).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3b25b0a-ae43-4671-b334-ec72999c55c5%2F1e681393-60ee-4704-a0a4-1a96e4ec07ba%2F75jv5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. [Hierarchical models] Some economic model assumes that individuals are heterogeneous in their
productivity factor. This factor can range between 0 and 1, and is uniformly distributed across the
economy. Thus, the productivity factor of a randomly selected individual is modeled with the uniform
random variable, X ~ U[0, 1]. An output produced by an individual is random, but depends on the
productivity, Y|X ~ B(n, X), where n is some natural number.
1
(a) Using the Law of Total Expectations find E(Y).
(b) Using the Law of Total Variances, find V(Y).
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