HW4sol - Online EE 131A Homework #4 Solution Fall 2010 K....

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Online EE 131A Homework #4 Solution Fall 2010 K. Yao 1. X is a random variable with a binomial distribution with parameter n and p = 0 . 9 a. Prob. the system will declare an airplane = P (1 X 2) = 1 - P ( X = 0) = 1 - ( 2 0 ) (0 . 9) 0 (0 . 1) 2 = 0 . 99 b. Prob. the system will declare an airplane = P (1 X 4) = 1 - P ( X = 0) = 1 - ( 4 0 ) (0 . 9) 0 (0 . 1) 4 = 0 . 9999 c. Prob. the system will declare an airplane = P (1 X n ) = 1 - P ( X = 0) = 1 - ( n 0 ) (0 . 9) 0 (0 . 1) n = 0 . 999 (0 . 1) n = 0 . 001 ⇐⇒ n = ln 0 . 001 ln 0 . 1 = 3 2. Let X = number of families out of 4 with incomes above $27 , 735. Then X has a binomial distribution with parameters n = 4 and p = 0 . 5. a. P ( X = 4) = ( 4 4 ) (0 . 5) 0 (0 . 5) 4 = 1 / 16 b. P ( X = 3) = ( 4 3 ) (0 . 5) 1 (0 . 5) 3 = 4 / 16 = 1 / 4 3. (a) 40! 30!5!3!2! ( . 6) 30 ( . 3) 5 ( . 07) 3 ( . 03) 2 (b) P (30 good, 4 fair, 6 others) = 40! 30!4!6!
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HW4sol - Online EE 131A Homework #4 Solution Fall 2010 K....

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