申論題

Question II (20 points, 10 points each)
Let Y denote a Bernoulli(θ) randon variable with 0 <θ < 1. Suppose we are interested in estimating the odds ratio, y = θ/(1-θ), which is the probability of success over the probability of failure. A nature estimator of y is, the proportion of successes over the proportion of failures in the sample. Note that , the proportion of successes in n trials, given a random sample{Y₁，Y₂,...Y_n}.