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( 0 (1 X) 1 X , 2) a For an event with probability p, the odds of the event is defined as p 1p 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) (1P (X 1 y)) What is the odds of disease if 1 0 What is the interpretation behind this result

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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}

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(₀(1 X) + ₁X , 2)

a. For an event with probability p, the odds of the event is defined as p/1p. 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)/(1P (X=1|y)). What is the odds of disease if ₁ = ₀? What is the interpretation behind this result?