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**noob mathematician** Under H0, a random variable has the cumulative distribution function $\displaystyle F_0(x)=x^2, 0\leq x\leq 1$; and under H1, it has the cumulative distribution function $\displaystyle F_1(x)=x^3, 0\leq x\leq 1$

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 $\displaystyle \frac{P(H_0|x)}{P(H_1|x)}=\frac{P(H_0)}{P(H_1)}\fr ac{P(x|H_0)}{P(x|H_1)}$, Given that the prior probability is equal will yield $\displaystyle \frac{P(H_0|x)}{P(H_1|x)}=\frac{P(x|H_0)}{P(x|H_1) }$ However, $\displaystyle x^2 \geq x^3$ 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