'4) (15 points) Let € be the parameter of a binomial distribution with 4 trials . Suppose that we use a single observation X to test Ho: 0 = 0.5 vs. H: 0 = 0.5. Show that the critical region {X=0,1,3 or 4} is unbiased.'
Added by Nicholas D.
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5. This can be done using the binomial distribution formula: P(X=k) = (4 choose k) * 0.5^4 where (4 choose k) is the number of ways to choose k successes out of 4 trials. For k=0,1,3,4, we have: P(X=0) = (4 choose 0) * 0.5^4 = 1/16 P(X=1) = (4 choose 1) * 0.5^4 Show more…
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