Suppose the proportion of left-handed individuals in apopulation is θ. Based on a simple random sample of 20, you observefour left-handed individuals. Using R
a) Assuming the sample size is small relative to the populationsize, plot the loglikelihood function and determine the MaximumLikelihood Estimate.
b) If instead the population size is only 50, then plot thelog-likelihood function and determine the MLE. (Hint: Remember thatthe number of left-handed individuals follows a hypergeometricdistribution. This forces θ to be of the form i/50 for some integeri between 4 and 34. From a tabulation of the log-likelihood, youcan obtain the MLE.)
