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# 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.) Suppose now that two of the choices are changed, so that X 1 ∼ N (6 . 0 , (1 . 5) 2 ) , X 4 ∼ N (7 . 5 , (2 . 4) 2 ) and X 5 ∼ N (8 . 0 , (3 . 0) 2 ) If the target lifetime t ( > 0, in thousands of hours) is arbitrary, which of these three circuits should
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