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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

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

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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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. Suppose p = .5. Find an expression for P(X = 1 | y) only in terms of fY|X(y | X = 1) and fY|X(y | X = 0), where fY |X represents the conditional normal density given above evaluated at some X = x.

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