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Unformatted text preview: STAT 3345 – PROBABILITY MODELS FOR ENGINEERS SPRING 2010 SAMPLE MIDTERM 2 EXAM Problem 1 The lifetime in hours of a certain kind of radio tube is a random variable having a probability density function given by f ( y ) = y < 100 100 y 2 if y > 100 . (a) Find the probability that the radio tube will have to be replaced within the first 150 hours of operation. (b) What is the probability that exactly 2 of 5 such tubes in a radio set will have to be replaced within the first 150 hours of operation? Assume that the events E i ,i = 1 , 2 , 3 , 4 , 5, that the i th such tube will have to be replaced within this time are independent. Problem 2 The completion time Y for a certain task has cumulative distribution function F ( y ) given by F ( y ) = y < y 4 4 ≤ y < 1 , 1- 1 20 (4- y )(6- y ) 1 ≤ y < 4 , 1 , y ≥ 4 ....
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This document was uploaded on 11/18/2010.
- Spring '09