In group testing for a certain disease, a blood sample was taken from each of n individuals and part of each sample was placed in a common pool. The latter was then tested. If the result was negative, there was no more testing and all n individuals were declared negative with one test. If, however, the combined result was found positive, all individuals were tested, requiring n+1 tests. If p = 0.05 is the probability of a person’s having the disease and n = 5, compute the expected number of tests needed, assuming independence.
Answer to relevant QuestionsSuppose that in Exercise 2.4-1, X = 1 if a red ball is drawn and X = −1 if a white ball is drawn. Give the pmf, mean, and variance of X. Show that 63/512 is the probability that the fifth head is observed on the tenth independent flip of a fair coin. Sketch the graphs of the following pdfs and find and sketch the graphs of the cdfs associated with these distributions (note carefully the relationship between the shape of the graph of the pdf and the concavity of the ...For each of the following functions, (i) Find the constant c so that f(x) is a pdf of a random variable X, (ii) Find the cdf, F(x) = P(X ≤ x), (iii) Sketch graphs of the pdf f(x) and the distribution function F(x), and ...Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x) = 0 for x ≤ 0 and 0 < F(x) < 1 for 0 < x. Prove that if P(X > x + y | X > x) = P(X > y), Then F(x) = 1 − e−λx, 0 < x. Which implies ...
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