Exercise 6. Consider a coin: Xi ~ B(0). We have n = 3 observations. We would like to decide whether 0 = 1/2 or 0 = 3/4.

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Exercise 6 Consider A Coin Xi B 0 We Have N 3 Observations We Would Like To Decide Whether 0 1 2 Or 0 3 4 1 (72.83 KiB) Viewed 25 times

Exercise 6. Consider a coin: Xi ~ B(0). We have n = 3 observations. We would like to decide whether 0 = 1/2 or 0 = 3/4. = 2 Ho : Q = 1/2, H: 0 = 3/4 a) Propose a likelihood ratio test d of size less than a = 5%. b) Estimate the type I and type II errors of the test 8 (resp. a(d) and B(6)). c) Find the likelihood ratio test that minimize the total error: a(8) + 5B(5). Estimate this error.