MidtermII_SOLN.WI02

MidtermII_SOLN.WI02 - NAME STAT 427 Prof Goel Midterm II...

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NAME:___________________________________ STAT 427 Midterm II Winter 2002 Prof. Goel MWF 11.30-12.30 Important: This exam is closed book/notes. You can use a calculator and a single-sided 8.5”x11” crib sheet. You must explain each step in your answer to get partial credits. Number of questions = 4. Total points = 50. Number of pages = 4. 1. a. [10 points] The ELISA test was developed in the mid 1980’s to screen blood samples for possible HIV (Human Immunodeficiency Virus) infection. Given an individual infected with the HIV infection, the test is positive 98% of the time. Further, given an individual without the HIV infection, the test is positive 7% of the time. Suppose 1% of all adults in a certain country have HIV infection. Compute the probability that a randomly selected individual in this county has the HIV infection given that the ELISA test for the selected individual is positive. NOTATIONS: IN {Selected Individual is HIV Infected} , POS {Elisa test result is Positive} Given, P[POS | IN] = 0.98, P[POS | N I ) = 0.07, P[IN] = 0.01 Therefore, P[ | IN) = 0.02, P[ S PO S PO | IN ] = 0.93, P[ N I ] = 0.99 Therefore, P[POS IN] = P[POS | IN] * P[IN] = 0.98 * 0.01 = 0.0098 I P[POS ] = P[POS | I N I N I ] * P[ N I ] = 0.07* 0.99 = 0.0693 P[POS] = P[POS IN] + P[POS I I N I ] = .0098 + .0693 = .0791 Hence, P[IN | POS] = P[POS] IN]
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