hw10 - ENEE 324 ASSIGNMENT 10 Due Tue 10/13 Problem 10A An...

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ENEE 324 ASSIGNMENT 10 Due Tue 10/13 Problem 10A An appliance uses one of three circuits ( i = 1 , 2 , 3). The lifetimes X i (in thousands of hours) of the three circuits have Gaussian distributions: X 1 ∼ N (6 . 0 , (1 . 5) 2 ) , X 2 ∼ N (6 . 5 , 1 . 5) 2 ) and X 3 ∼ N (7 . 0 , (1 . 5) 2 ) (i) (6 pts.) For each circuit, determine the probability that its lifetime exceeds ( a ) 7,500 hours; ( b ) 8,000 hours. In each case, give an expression in terms of Q ( · ) (or Φ( · )), as well as the numerical value. (ii) (6 pts.) Suppose the prices of the three circuits are $8.00, $9.00 and $11.00 respectively, and that the target lifetime is 5,000 hours. If a circuit fails before that, then the appliance is refunded at $20.00. The expected overall cost to the manufacturer is there c i + 20 p i , where c i is the circuit cost and p i is the probability that the lifetime is less than 5,000 hours. Which of the three circuits should the manufacturer use in order to minimize the expected cost? (iii) (8 pts.)
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This note was uploaded on 03/21/2010 for the course ENEE 324 taught by Professor Ephrimedes during the Fall '05 term at Maryland.

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