Stat W 4201 Assignment #9 solved

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1. Chapter 20, problem 12
2. Chapter 21, problem 16
3. Suppose that a population of individuals is partitioned into sub-poplations or groups, G1 and G2.
It may be helpful to think of G1 in an epidemiological context as the carriers of a particular virus,
comprising 100π1% of the population, and G2 as the non-carriers. Measurements Z made on individuals
have the following distributions in the two groups:
G1 : Z ∼ N(µ1, Σ)
G2 : Z ∼ N(µ2, Σ).
Let z be an observation made on an individual drawn at random from the combined population. The
prior odds that the individual belongs to G1 are π1/(1 − π1). Show that the posterior odds given z are
1 − π1
exp(α + β
and give the form of α and β. For more discussion on logistic discrimination and linear discriminant
analysis, see Efron (1975). The efficiency of logistic regression compared to normal discriminant analysis
(1975). Journal of the American Statistical Association 70, 892-898.