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# ch03 - CHAPTER 3 Section 3-1 3-1 The range of X is...

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CHAPTER 3 Section 3-1 3-1. The range of X is { } 1000 ,..., 2 , 1 , 0 3-7. The range of X is conveniently modeled as all nonnegative integers. That is, the range of X is { } 012 , , ,... Section 3-2 3-15. All probabilities are greater than or equal to zero and sum to one. a) P(X 2)=1/8 + 2/8 + 2/8 + 2/8 + 1/8 = 1 b) P(X > - 2) = 2/8 + 2/8 + 2/8 + 1/8 = 7/8 c) P(-1 X 1) = 2/8 + 2/8 + 2/8 =6/8 = 3/4 d) P(X -1 or X=2) = 1/8 + 2/8 +1/8 = 4/8 =1/2 3-21. X = number of wafers that pass P(X=0) = (0.2) 3 = 0.008 P(X=1) = 3(0.2) 2 (0.8) = 0.096 P(X=2) = 3(0.2)(0.8) 2 = 0.384 P(X=3) = (0.8) 3 = 0.512 3-25. P(X = 15 million) = 0.6, P(X = 5 million) = 0.3, P(X = -0.5 million) = 0.1 Section 3-3 3-31. < < < < = x x x x x x F 3 , 1 3 2 , 488 . 0 2 1 , 104 . 0 1 0 , 008 . 0 0 , 0 ) ( where , 512 . 0 ) 8 . 0 ( ) 3 ( , 384 . 0 ) 8 . 0 )( 8 . 0 )( 2 . 0 ( 3 ) 2 ( , 096 . 0 ) 8 . 0 )( 2 . 0 )( 2 . 0 ( 3 ) 1 ( , 008 . 0 2 . 0 ) 0 ( . 3 3 = = = = = = = = f f f f 3-37. The sum of the probabilities is 1 and all probabilities are greater than or equal to zero; pmf: f(-10) = 0.25, f(30) = 0.5, f(50) = 0.25 a) P(X 50) = 1 b) P(X 40) = 0.75 c) P(40 X 60) = P(X=50)=0.25 d) P(X<0) = 0.25 e) P(0 X<10) = 0 f) P( - 10<X<10) = 0 3-1

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3-41. Determine E(X) and V(X) for random variable in exercise 3-15 . 0 ) 8 / 1 ( 2 ) 8 / 2 ( 1 ) 8 / 2 ( 0 ) 8 / 2 ( 1 ) 8 / 1 ( 2 ) 2 ( 2 ) 1 ( 1 ) 0 ( 0 ) 1 ( 1 ) 2 ( 2 ) ( = + + + - - = + + + - - - - = = φ φ φ φ φ Ξ Ε μ 5 . 1 0 ) 8 / 1 ( 4 ) 8 / 2 ( 1 ) 8 / 2 ( 0 ) 8 / 2 ( 1 ) 8 / 1 ( 4 ) 2 ( 2 ) 1 ( 1 ) 0 ( 0 ) 1 ( 1 ) 2 ( 2 ) ( 2 2 2 2 2 2 2 = - + + + + = - + + + - - - - = μ φ φ φ φ φ Ξ ς 3-49. X = number of computers that vote for a left roll when a right roll is appropriate.
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