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Module 4 assignment

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Question;Antibodies present 0.9985 0.0015;Antibodies absent 0.006 0.994;Suppose that I% of a large population carries antibodies to HIV in their blood.;(a);Draw a tree diagram for selecting a person;from this population (outcomes: antibodies;present or absent) and for testing his or her blood;(outcomes:ETA positive or negative).;(b) What is the probability that the EIA is positive for a randomly chosen person from this population?;(c);What is the probability that a person has;the antibody, given that the BIA test is;positive?(Comment:This exercise illustrates a fact that is important when considering proposals for wide spread testing for HIV, illegal, drugs, or agents of biological warfare: if the condition being tested is uncommon in the population, many positives will be false-positives,);ting for HIV, continued. The previous;exercise Ives data on the results of EIA tests for the presence of antibodies;to HIV. Repeat part (c) of that exercise for two;different populations;(a);Blood donors are prescreened for HIV risk factors, so perhaps only 0.1% (0.001) of this.population carries HIV antibodies.;(b);Clients of a drug rehab clinic are a;high-risk group, so perhaps 10% of this population;carries I-11V antibodies.;(c);What general lesson do your calculations illustrate?;The geometric distributions. You are tossing;a balanced die that has probability 1/6 of;coming up1 on each toss. Tosses are independent. We;are;interested in how long we must wait to get;the first 1.;(a) The probability of a 1 on the first toss is 1/6_ What is the;probability that the first toss is not a I and the second toss is a 1?;(b) What is;the probability that the first two tosses are not is and the third toss is a 1?;This is the probability that the first 1 occurs on the third toss.

 

Paper#61703 | Written in 18-Jul-2015

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