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Problem #5 Draw a county at random from the state of Maryland. Then, draw n people at random from the county. Let X be the number of those people who have tested positive for COVID-19. If Q denotes the proportion of people in that county with COVID-19, then Q is also a random variable since it varies from county to county. Given Q = q, we have that X - Binomial(n, q). Thus, E(X |Q = q) = nq and Var( X | Q = q) = nq(1-q). Suppose that the random variable Q has a Uniform(0, 1) distribution. A distribution that is constructed in stages like this is called a hierarchical model and can be written as Q ~ Uniform(0, 1) X|Q = q~ Binomial(n, q). Then, find E(X) and Var(X).

Problem #5 Draw a county at random from the state of Maryland. Then, draw n people at random from the county. Let X be the number of those people who have tested positive for COVID-19. If Q denotes the proportion of people in that county with COVID-19, then Q is also a random variable since it varies from county to county. Given Q = q, we have that X - Binomial(n, q). Thus, E(X |Q = q) = nq and Var( X | Q = q) = nq(1-q). Suppose that the random variable Q has a Uniform(0, 1) distribution. A distribution that is constructed in stages like this is called a hierarchical model and can be written as Q ~ Uniform(0, 1) X|Q = q~ Binomial(n, q). Then, find E(X) and Var(X).

MATLAB: An Introduction with Applications
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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Problem #5 Draw a county at random from the state of Maryland. Then, draw n people at random from the county. Let X be the number of those people who have tested positive for COVID-19. If Q denotes the proportion of people in that county with COVID-19, then Q is also a random variable since it varies from county to county. Given Q = q, we have that X - Binomial(n, q). Thus, E(X |Q = q) = nq and Var( X | Q = q) = nq(1-q). Suppose that the random variable Q has a Uniform(0, 1) distribution. A distribution that is constructed in stages like this is called a hierarchical model and can be written as Q ~ Uniform(0, 1) X|Q = q~ Binomial(n, q). Then, find E(X) and Var(X).
Transcribed Image Text:Problem #5 Draw a county at random from the state of Maryland. Then, draw n people at random from the county. Let X be the number of those people who have tested positive for COVID-19. If Q denotes the proportion of people in that county with COVID-19, then Q is also a random variable since it varies from county to county. Given Q = q, we have that X - Binomial(n, q). Thus, E(X |Q = q) = nq and Var( X | Q = q) = nq(1-q). Suppose that the random variable Q has a Uniform(0, 1) distribution. A distribution that is constructed in stages like this is called a hierarchical model and can be written as Q ~ Uniform(0, 1) X|Q = q~ Binomial(n, q). Then, find E(X) and Var(X).
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