Consider a sequence of independent tosses of a coin, and let $P_h$ be the probability of a head on any toss. Let $A$ be the hypothesis that $P_h = a$, and let $B$ be the hypothesis that $P_h = b$. Let $X_i$ be the outcome of the i:th toss, and set $$Z_n = \frac{P\{X1,...,Xn|A\}}{P\{X1,..., Xn|B\}}$$ I was just wondering then if $P_h = b$, is it true that $Z_n,n \geq 1$, is a martingale having mean 1 with respect to $X_n,n \geq 1$?
If it is then can someone show me how?
Thanks in advance.