~HW1_2_Sol

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ECEN 646 Homework 1, Part 2 Solutions 4 C ¸inlar Exercise (4.7), Chapter 1 For a real root, we need to have that B 2 - 4 AC 0. Combinations of A, B, and C satisfying B 2 4 AC , and their probabilities are as follows: B = - 3 ,A = 1 ,C = 1, with probability (0 . 25)(0 . 4)(0 . 5) = 0 . 05. B = - 3 ,A = 1 ,C = 2, with probability (0 . 25)(0 . 4)(0 . 4) = 0 . 04. B = - 3 ,A = 2 ,C = 1, with probability (0 . 25)(0 . 6)(0 . 5) = 0 . 075. B = - 2 ,A = 1 ,C = 1, with probability (0 . 25)(0 . 4)(0 . 5) = 0 . 05. Note that probabilities multiply because A, B, and C are independent random variables. Because the four are disjoint, add their probabilities to get that P ( B 2 - 4 AC 0) = 0 . 215. 5 C ¸inlar Exercise (4.8), Chapter 1 The reliability of the equipment for 4000 hours is the probability that all three components last 4000 hours, ie., P ( { X 1 4000 } ∩ { X 2 4000 } ∩ { X 3 4000 } ) = P { X 1 4000 } P { X 2 4000 } P { X 3 4000 } = (1 - P { X 1 4000 } )(1 - P { X 2 4000 } )(1 - P { X 3 4000 } ) = exp( - 0 . 4) exp( - 0 . 8) exp( - 0 . 12) = exp( - 1 . 32) 0 . 267 6 Additional Problem Since P [ { ω i } ] = 0
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  • Fall '16
  • dcdc
  • Probability theory, sh, inlar Exercise

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