Bernoulli trials

- The alternatives are indexed by an \(x\) running from 1 through 15 .

- The prior probability in choosing among the 15 alternatives is uniform.

- For alternative \(x\), we have \(P(\mathrm{~T})=x / 15\) whereas \(P(\perp)=1-P(\mathrm{~T})\).

- You perform two trials, "with replacement"; the outcome is \(T \perp\).

(a) Write down the function \(f(x)\) describing the prior probabilities of getting alternative \(x\).

(b) Find the likelihood function \(g(x)\).

(c) Fill in the table to find the posterior probability that you got alternative \(x\).

(d) What is the probability that the next trial yields T?