MidtermII_SOLN.WI02

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

This preview shows pages 1–2. Sign up to view the full content.

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]

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern