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 Xis 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.p =If n = 20 and x = 5, what is the estimate?p=(b) Is the estimator of part (a) unbiased?YesNo(c) If n = 20 and x = 5, what is the mle of the probability (1 − p)5 that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.)

We have given that Let X = the number among the n test results that are positive p = probability…

Answered: A diagnostic test for a certain disease…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal with a mean u= 7500 and a = 1750. A test result of x < 3500 is an indication of leucopenia. This indicates bone marrow depression that may result in a viral infection. a. What is the probability that on a single test x is less than 3500? b. A patient is given 3 tests at regular intervals. What is the probability that the average of the three tests is less than 3500?
Let Y be the number of successes in n independent trials of a random experiment having probability of success . For n = 5, compute P(Y > 3).
A survey showed that 83% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 18 adults are randomly selected, find the probability that at least 17 of them need correction for their eyesight. Is 17 a significantly high number of adults requiring eyesight correction? ... The probability that at least 17 of the 18 adults require eyesight correction is (Round to three decimal places as needed.)
In a sample of 900 U.S. adults, 210 think that most celebrities are good role models. U.S. adults are selected from this sample without replacement. Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is enter your response here. (Round to three decimal places as needed.)
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 Xi 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? Yes 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-free individuals are positive? (Round your answer to four decimal places.)
It is known that in a certain town 30% of the people own an Kpfone. A researcher asks people at random whether they own an Kpfone. The random variable X represents the number of people asked up to and including the first person who owns an Kpfone. Determine that P(X <6).
There are 100 multiple-choice question on exam, each having responses a, b, c, d. suppose that a student has 75% chance to answer each qustion correctly and all the answers are independent. if the student needs to answer at least 40 questions to pass, what is the probability that the student passes? Use normal approximation.
A certain type of cancer is known to exist in 2 percent of the population of the males in their fifties. A test for the disease has been is advertised by a pharmaceutical company to have sensitivity 0.97 and specificity 0.95. A male is randomly selected from this population, and tested. The test result is negative. First determine the probability this male has the cancer.
A survey showed that 81% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 20 adults are randomly selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction? The probability that no more than 1 of the 20 adults require eyesight correction is (Round to three decimal places as needed.)
The table summarizes results from 986 pedestrian deaths that were caused by automobile accidents. DriverIntoxicated? Pedestrian Intoxicated? Yes No Yes 58 81 No 240 607 If two different pedestrian deaths are randomly selected, find the probability that they both involved drivers that were intoxicated.
A survey showed that 79% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 15 adults are randomly selected, find the probability that at least 14 of them need correction for their eyesight. Is 14 a significantly high number of adults requiring eyesight correction? The probability that at least 14 of the 15 adults require eyesight correction is nothing. (Round to three decimal places as needed.)
A large bag contains pretzels with 3 different shapes: heart, square, circle . Billy plans to reach into the bag and draw out one pretzel at a time, stopping only when he has at least one pretzel of each type. Let the random variable X denote the number of pretzels that Billy will draw from the bag. You can assume that there is an infinite number of pretzels in the bag with equal proportions of each shape. Find E(X).

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