A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the ntest results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability thata disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that arepositive). Assume that only X is available rather than the actual sequence of test results.(a) Derive the maximum likelihood estimator of p.p =If n = 20 and x = 7, what is the estimate?p =(b) Is the estimator of part (a) unbiased?YesO No(c) If n = 20 and x = 7, what is the mle of the probability (1 - p)5 that none of the next five tests done on disease-freeindividuals are positive? (Round your answer to four decimal places.)Need Help? Read It

Let X= the number among the n test results that are positive.X is the number of false positives). is the probability that a disease-free individual's test result is positive.In the given scenario, the random variable X has a binomial distribution with parameters and .Thus, the likelihood function is given by:Apply natural logarithm to the likelihood function is:Differentiative with respect to p as shown below:Equate this derivative to 0:Thus, the likelihood estimator of is Given: and .The estimate of is:The estimator of part (a) is unbiased, because:Thus, the answer is Yes.(c) The maximum likelihood estimator of is .Given; , the mile of the probability that none of the next five tests done on disease free individuals are positive is:(a) The estimate of is: (b) Yes(c)