Question
In: Math
A diagnostic test for a certain disease is applied to n individuals known to not have...
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 = 7, what is the estimate?
(b) Is the estimator of part (a) unbiased?
(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.)
Solutions
milcah answered 2 years agoRelated Solutions
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Consider a diagnostic test for a hypothetical disease based on measuring the amount of a certain...
Consider a diagnostic test for a hypothetical disease based on
measuring the amount of a
certain biomarker present in blood. High levels of the biomarker
are often found in individuals
with the disease, but a number of non-disease conditions can
also cause high levels
of the biomarker. Individuals without the disease have biomarker
levels that are normally
distributed with mean 1.6 ng/mL (nanograms per milliliter of
blood), and standard deviation
0.50 ng/mL. Individuals with the disease have biomarker levels
that...
Consider a diagnostic test for a hypothetical disease based on measuring the amount of a certain...
Consider a diagnostic test for a hypothetical disease based on
measuring the amount of a certain biomarker present in blood. High
levels of the biomarker are often found in individuals with the
disease, but a number of non-disease conditions can also cause high
levels of the biomarker. Individuals without the disease have
biomarker levels that are normally distributed with mean 1.6 ng/mL
(nanograms per milliliter of blood), and standard deviation 0.50
ng/mL. Individuals with the disease have biomarker levels that...
Consider a diagnostic test for a hypothetical disease based on measuring the amount of a certain...
Consider a diagnostic test for a hypothetical disease based on
measuring the amount of a certain biomarker present in blood. High
levels of the biomarker are often found in individuals with the
disease, but a number of non-disease conditions can also cause high
levels of the biomarker. Individuals without the disease have
biomarker levels that are normally distributed with mean 1.6 ng/mL
(nanograms per milliliter of blood), and standard deviation 0.50
ng/mL. Individuals with the disease have biomarker levels that...
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28.
A diagnostic test has a probability 0.95 of giving a positive
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and a probability 0.10 of giving a (false) positive when applied to
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