source('https://myweb.uiowa.edu/pbreheny/7110/f20/notes/fun.R')

n <- 12
x <- 100
mu <- x/n
theta <- log(mu)
v <- 1/mu
CI <- theta + qnorm(c(.025, .975))*sqrt(v/n)
exp(CI)
poisson.test(x, n)$conf.int

# Coef of var
xx <- seq(-3, 3, length=101)
plot(xx, xx^2, col='slateblue', type='l', bty='n', lwd=3, xlab=expression(mu), ylab=expression(sigma^2), las=1)