function y = lnbernoufoc(r,x);
% This is the FOC w.r.t. r of the log likelihood function for X ~ Bernoulli(p)
%--------------------------------------------------------------
% OUTPUT: y = value of the partial of the log likelihood function w.r.t r
% INPUT:  r = Bernoulli parameter, we've diff w.r.t. it to get the FOC.
%         x = vector of iid Bernoulli draws

%Strangly, we've found that variables of interest need to be included as "r
%subscript 1" which in MatLab is "r(1)". We had to do this even though we
%only have one variable.

m = size(x,1);
xbar = mean(x);

y = m*xbar/r(1) - m*(1-xbar)/(1-r(1));