From 1965 to 1974, in U.S. there were M = 17, 857, 857 male livebirths and F = 16, 974, 194 female livebirths. We model the number of male livebirth as a binomial distribution with parameters size = M+F and prob = p. The following code computes the maximum likelihood estimator for p. M 17857857 F IL.ps Oe+00 -2e+07 -4e+07 -6e+07 0.0 0.2 0.4 ps 0.6 0.8 1.0 a.) What is the use of the parameter log=TRUE in the definition of function II? b.) Is II the likelihood function or the log-likelihood function? (I already answered this one as log-likelihood c.) An estimator for p, denoted by p^, is obtained by ps[which.max(II.ps)]. Is this the maximum likelihood estimator? Why (explain the code)? d.) What can we learn from this plot e.) For this problem, can you give a theoretical formula for the maximum likelihood estimator, p^, using M and F? (no need to compute numerical value.)