Under H
0, 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 H
0 greater than that of H
1?
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