Answer part a 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. For an event with probability p, the odds of the event is defined as p/1−p. With a higher odds, an event is more likely. With the odds of 1 indicates the event is as likely to occur as not likely. i.e. we are maximally uncertain about the status of the diseae. Find the conditional odds of disease given Y ,P(X=1|y)/(1−P (X=1|y)). What is the odds of disease if µ1 = µ0?What is the interpretation behind this result?

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Answered: Answer part a of the question below.…

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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Answer part a 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. For an event with probability p, the odds of the event is defined as p/1−p. With a higher odds, an event is more likely. With the odds of 1 indicates the event is as likely to occur as not likely. i.e. we are maximally uncertain about the status of the diseae. Find the conditional odds of disease given Y ,
P(X=1|y)/(1−P (X=1|y)). What is the odds of disease if µ₁ = µ₀?
What is the interpretation behind this result?

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