psiConfidenceInterval = function() {

negLL = function(psi) (-1)*dbinom(z, size=n, prob=psi, log=T)

z = 1
n = 5
fit = optim(0.5, negLL, method='BFGS', hessian=TRUE)

psi.mle = fit$par
psi.se = sqrt(1/fit$hessian)
zcrit = qnorm(.975)
c(psi.mle-zcrit*psi.se, psi.mle+zcrit*psi.se)
}