Question: A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the

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 disease free 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?

Step by Step Solution

★★★★★

3.45 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a To find the mle of p well take the derivative of the loglikelihood function Set ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

1172-M-S-P-E(1209).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

A screening test for a certain disease is prone to giving false positives or false negatives. If a patient being tested has the disease, the probability that the test indicates a (false) negative is...

A pharmaceutical company has developed a diagnostic test for a rare disease. The test has sensitivity 0.99 (the probability of testing positive among people with the disease) and specificity 0.995...

For a diagnostic test of a certain disease, 1 denotes the probability that the diagnosis is positive given that a subject has the disease, and 2 denotes the probability that the diagnosis is...

please show work: 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...

A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let * = the number among the n test results that are positive (indicating presence of the disease,...

Problem 3. 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...

A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the 1': test results that are positive (indicating presence of the disease,...

1. A new diagnostic test for a certain disease is evaluated. The test was performed on 300 individuals known to have the disease and correctly identified 240 of them as positive. It was also...

Ho 2.19) As discussed in Exercise 2.11. in a class of 60 students. 13 could not roll their tongue, 17 had attached earlobes, and 10 could roll their tongues and had attached earlobes. A student is...

At July 31, Farmer Company has this bank information: cash balance per bank $7,291; outstanding checks $762; deposits in transit $1,350; and a bank service charge $40. Determine the adjusted cash...

Use the information from the preceding sentences to write a coherent paragraph about replacing the sports scoreboard. Strive to use three devices to build coherence: (a) Repetition of key words, (b)...

Which of the following will increase the supply of loanable funds? a. an increase in perceived business opportunities b. decreased government borrowing c. an increased private saving rate d. an...

What will getting what you want confirm about you as a person/professional?

Qualifications of male and female head and assistant college athletic coaches were compared in the article Sex Bias and the Validity of Believed Differences Between Male and Female Interscholastic...

A study in the Journal of Marketing Research investigated the relationship between facility conditions at gas stations and aggressiveness in the pricing of gasoline. The accompanying data is based on...

Three assembly lines for the same product have different nonconformance rates: p = .1 for Line A, p = .15 for Line B, and p = .2 for Line C. One of the three lines will be selected at random (but you...

The price of Cilantro, Incorporated, stock will be either $65 or $87 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 3 percent. a. Suppose the...

1. Descriptive Statistics (Measures of Can trai Tendency) A. Analyze the following situation about "Teacher Salaries" and answer the given questions. Show your complete solution [if necessary)....

Question 2 A hurricane policy covers both water damage, X, and wind damage, Y, where X and Y have joint density function f(x, y) = 0.13e-0-53-0.29 - 0.06e-3-0.2y _ 0.06e-0-53-049 4 0.12e-3-043, +...