Let $X_0, X_1, ...$ i.i.d random variables.
Show that $$M_n = \frac{e^{\theta(x_0 + ... + x_n)}}{E[e^{\theta x_1}]}$$
is a martingale to respecto to $F^S$
I'm trying to prove that $E[M_n]<\infty$ and I know that somehow I how to use that they are identical and independent random variables but I'm not sure how to deal with the denominator. Any suggestions would be great!