The probability of Heads of a coin isy, and this biasyis itself the realization of a random variableY which is uniformly distributed on the interval[0,1].

To estimate the bias of this coin. We flip it6times, and define the (observed) random variableNas the number of Heads in this experiment.

What is the LMS estimate ofY, givenN=3?

Throughout this problem, you may find the following formula useful: For every positive integers n, k, n!k! x" (1 - x)k dx = 0 (n+ k+ 1 )!'