The answer as given is 2/3. But I not sure how to get it
Under H0, a random variable has the cumulative distribution function ; and under H1, it has the cumulative distribution function
Question: If the two hypotheses have equal prior probability, for what values of x is the posterior probability of H0 greater than that of H1?
This is what I did:
Since I know that , Given that the prior probability is equal will yield However, given that 0<x<1, so it seems that for all values the statement is true, but the answer is apparent not as above.
Hope someone can help me. Thanks
The answer is . Anyone can help with the explanation?
My understanding is as followed: to find power of the test, I will use
Can it be that the answer is wrong, which is highly impossible i think.