If you have:

X - Binomial(n,\theta)

H_0 : \theta = \theta_0
H_a : \theta \neq \theta_0

p(H_0) = \pi
p(H_a) = 1-\pi


given H_a, \theta is Beta(\alpha,\beta)

what is

<br /> \frac{p(x | H_0)}{p(x | H_a)} ?<br />

I know p(x | H_0) but how do you derive the p(x | H_a)?

Thanks for any help.