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We start with the case in which each subexperiment is a trial with sample space S = {0, 1} indicating failure or success. 38 For five subexperiments with sample space S = {0, 1}, how many observation sequences are there in which 0 appears n 0 = 2 times and 1 appears n 1 = 3 times? The set of five-letter words with 0 appearing twice and 1 appearing three times is {00111, 01011, 01101, 01110, 10011, 10101, 10110, 11001, 11010, 11100}. There are exactly 10 such words. 38 and making sure that no sequences are overlooked is surprisingly difficult.

This model implies an experiment in which the procedure is to monitor a call and the observation consists of the type of call, v, d, or f , and the length, l or b. The sample space has six outcomes S = {lv, bv, ld, bd, l f, b f }. In this problem, each call is classifed in two ways: by length and by type. Using L for the event that a call is long and B for the event that a call is brief, {L , B} is an event space. Similarly, the voice (V ), data (D) and fax (F) classification is an event space {V, D, F}.

8 3 Independent Events A1 , A 2 , and A 3 are independent if and only if (a) A 1 and A 2 are independent, (b) A 2 and A 3 are independent, (c) A 1 and A 3 are independent, (d) P[ A 1 ∩ A2 ∩ A3 ] = P[ A 1 ]P[ A 2 ]P[ A 3 ]. 7. The following example shows why this condition is insufficient to guarantee that “everything is independent of everything else,” the idea at the heart of independence. 23 In an experiment with equiprobable outcomes, the event space is S = {1, 2, 3, 4}. P[s] = 1/4 for all s ∈ S.

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Accuracy of MSI testing in predicting germline mutations of MSH2 and MLH1 a case study in Bayesian m by Chen S.

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