In order to solve (c), I think I need a plot of the log-likelihood of the binomial distribution. Can anyone please help me do it in R? The data and the question is as follows;
I think I need this kind of plot:
Something like this should work:
F <- c(18,31,34,33,27,33,28,23,33,12,19,25,14,4,22,7) M <- c(11,22,27,29,24,29,25,26,38,14,23,31,20,6,34,12) Y <- F N <- F + M #a) Y / N #b) sum(Y) / sum(N) #c) logL <- function(p) sum(log(dbinom(Y, N, p))) #plot logL: p.seq <- seq(0.01, 0.99, 0.01) plot(p.seq, sapply(p.seq, logL), type="l") #optimum: optimize(logL, lower=0, upper=1, maximum=TRUE)
As noted by Ben (see comments), the numerical accuracy is increased by the use of:
logL <- function(p) sum(dbinom(Y,N,p,log=TRUE)) instead, especially it can "rescue" you in cases where
dbinom() returns 0 but the likelihood-score is actually just close to 0.