A company sells multivitamin tablets, claiming that they reduce the probability of getting a cold by 90%. To evaluate the true efficacy of the the tablets, a clinical-trials organisation tests the tablets in n healthy volunteers.
For each volunteer, let α denote the probability of getting a cold while on a course of the tablets, and let $β$ denote the probability of getting a cold while not on a course of the tablets. Suppose $$α=(1−a)β,$$ where a denotes the efficacy of the tablets, $0≤a≤1$ . If the tablets are as effective as the company claims, then $a=0.9$ .
Suppose, before the trial beings, you believe the efficacy $a$ of the tablets lies with Uniform probability anywhere between 0 and 0.9. Suppose each of the $n$ volunteers catches a cold during the trial, independently of all others. Derive your posterior pdf for $a$ as a function of the number of volunteers, n .
For the case of $n=10$ , evaluate your posterior pdf for $a$ for each value of $a∈{\{0,0.1,0.2,…,1\}}$ , entering your answers to 3 decimal places.
Could you please steer me in the right direction, my whole class is lost and so am I. This has to do with posterior distribution.