I have to prove with a simple example and a plot how prior beta distribution is conjugate to the geometric likelihood function. I know the basic definition as
'In Bayesian probability theory, a class of distribution of prior distribution $\theta$ is said to be the conjugate to a class of likelihood function $f(x|\theta)$ if the resulting posterior distribution is of the same class as of $f(\theta)$.'
But I don't know how to prove it mathematically.
P.S. - It would really nice of you guys to provide some good material on bayesian statistic and probability theory.