Suppose we toss a coin which is not fair. and the probability of success is 0.7. Is that enough to decide on the shape of it beta distribution ? what would be its shape then ?
As far as I know, it's the probability of success that we map in the X-axis. so, it should be between 0 and 1. But in some articles and books I've found, x axis has some values beyond that. I'm confused.
Please help
Answer:
Tossing an unfair coin N times with a probability of success being r and you get $N_{1}$ times heads and $N_{2}$ times tail follows a beta distribution and the pmf is given by
$$ \dfrac{r^{N_{1}}(1-r)^{N_{2}}}{\beta(N_{1}+1,N_{2}+1)}$$
$N_{1}$ and $N_{2}$ define the shape parameters of the beta distribution. It is r that decides the peak. r alone does not describe the distribution. r should lie between 0 <= r <= 1