From 1965 to 1974, in U.S. there were M = 17, 857, 857 male livebirths and...

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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 <- 16974194 11 <-function(p){ dbinom (M, size=M+F, prob=p, log=TRUE)) ps <- seq(0.01, 0.99, by = 0.001) 11.ps <- 11(ps) plot(ps, ll.ps, type='1') phat <- ps[which.max(ll.ps)] abline(v=phat, col='blue') 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.) 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 <- 16974194 11 <-function(p){ dbinom (M, size=M+F, prob=p, log=TRUE)) ps <- seq(0.01, 0.99, by = 0.001) 11.ps <- 11(ps) plot(ps, ll.ps, type='1') phat <- ps[which.max(ll.ps)] abline(v=phat, col='blue') 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.)