Answer parts a and b of the question below. Show all work. When diagnosing a disease (genetically) in a sample of patients. we let X ∈ {0, 1} be a random variable that is binary where X = 1 reflects disease presense, and X = 0 reflects absense of the disease. We are conducting a blood test that returns some continuous marker. A continuous variable expressing this marker is −∞ < Y < ∞. We then use the following hierarchical
Answer parts a and b of the question below. Show all work. When diagnosing a disease (genetically) in a sample of patients. we let X ∈ {0, 1} be a random variable that is binary where X = 1 reflects disease presense, and X = 0 reflects absense of the disease. We are conducting a blood test that returns some continuous marker. A continuous variable expressing this marker is −∞ < Y < ∞. We then use the following hierarchical
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Answer parts a and b of the question below. Show all work.
When diagnosing a disease (genetically) in a sample of patients.
we let X ∈ {0, 1} be a random variable that is binary where X = 1 reflects disease presense, and X = 0 reflects absense of the disease. We are conducting a blood test that returns some continuous marker. A continuous variable expressing this marker is −∞ < Y < ∞. We then use the following hierarchical model:
X ∼ Ber(p)
Y | X ∼ N(µ0(1 − X) + µ1X , σ2)
a. Find Cov(Y, X).
b. Find the marginal variance, V [Y], in terms of p, µ1, µ0, and σ2
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