Statistical Problem

Isidor has been gifted a coin from his grandfather. Let p be the probability that on any given flip of the coin, it lands with heads up. Before conducting any flips of the coin, Isidor has no clue whatsoever as to the value of p
(a) What is a reasonable prior distribution Isidor can use to model his current cluelessness about p? (Hint: Keep it simple and uninformative.

(b) Isidor now conducts 10 procedurally identical flips of the coin. On each flip, the coin has probability p of landing heads up. And when it does, Isidor records a 1. Otherwise he records a 0. The result is {1,0,1,1,1,1,1,0,1,1}. Let the ith flip be denoted Xị. Given this setup, a reasonable likelihood model for the flips is: X1, …, X10 are independent (given p) and identically distributed under a Bernoulli distribution with parameter p, specifically where Pr(X; = 1|p) = p and Pr(X; = 0p) = 1 - p. Using this likelihood, and the prior in (a), what value of p gives the most likely model?

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