Statistics Homework Solutions 52

Statistics Homework Solutions 52 - 52 CHAPTER 2 35(a If the...

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52 CHAPTER 2 35. (a) If the pooled test is negative, it is the only test performed, so X 1. If the pooled test is positive, then n additional tests are carried out, one for each individual, so X n 1. The possible values of X are therefore 1 and n 1. (b) The possible values of X are 1 and 5. Now X 1 if the pooled test is negative. This occurs if none of the individuals has the disease. The probability that this occurs is 1 0 1 4 0 6561. Therefore P X 1 0 6561. It follows that P X 5 0 3439. So μ X 1 0 6561 5 0 3439 2 3756. (c) The possible values of X are 1 and 7. Now X 1 if the pooled test is negative. This occurs if none of the individuals has the disease. The probability that this occurs is
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