A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a diseasefree individual’s test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results.a. Derive the maximum likelihood estimator of p. If n = 20 and x = 3, what is the estimate?b. Is the estimator of part (a) unbiased?c. If n = 20 and x = 3, what is the mle of the probability (1 - p)5 that none of the next five tests done on disease-free individuals are positive?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the
a. Derive the maximum likelihood estimator of p. If n = 20 and x = 3, what is the estimate?
b. Is the estimator of part (a) unbiased?
c. If n = 20 and x = 3, what is the mle of the probability (1 - p)5 that none of the next five tests done on disease-free individuals are positive?
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