(i) For a binary response y, let y be the proportion of ones in the sample (which is equal to the sample average of the y.). Let 0 be the percent correctly predicted for the outcome y = 0 and let 1 be the percent correctly predicted for the outcome y = 1. If p is the overall percent correctly predicted, show that p is a weighted average of 0 and 1:

(ii) In a sample of 300, suppose that = .70, so that there are 210 outcomes with yt = 1 and 90 with yt = 0. Suppose that the percent correctly predicted when yt = 0 is 80, and the percent correctly predicted when yt = 1 is 40. Find the overall percent correctly predicted.

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p = (1- ) +y-