I have this problem: In betting situations one is often interested in odds, referring in the thumbtack tossing $\theta / (1 - \theta)$. Alternatively one may consider the log-odds:
Show that a uniform distribution for $\lambda$ implies the following distribution for $\theta$:
What problems are associated with this distribution if it is used as a prior in the thumbtack tossing problem?
Now I have the thumbtack thingy, I know what it will happen if we use that p as prior, but the uniform for $\lambda$ implies the p($\theta$) I don't get it, I have tried to get to the p($\theta$) from both sides but I always get to $log(\theta)-log(1-\theta)$ and can't get out, any help??