Say I have a number little n of books. If I throw them up, they will land either with their front or their back up. Say they all have the same probability to land with their front up, denoted by q, which is random and uniform between 0 and 1. All throws are independent. Say also, that we have for each book a random variable B_i, that stands for the number of throws until the i'th book first lands with its front up. B_i includes the throw that is the first one with front up. I know the PMF of B_1, but I need a LMS estimate of Q, which I base on the little b that I observe for B_1. I know this is the same as E[Q|B_1=b] = an integral over q times the posterior probability of Q given T_1