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Unformatted text preview: CHAPTER 3 Section 31 31. The range of X is { } 1000 ,..., 2 , 1 , 37. The range of X is conveniently modeled as all nonnegative integers. That is, the range of X is { } 012 , , ,... Section 32 315. 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 =1/2 321. 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 = 0.512 325. P(X = 15 million) = 0.6, P(X = 5 million) = 0.3, P(X = 0.5 million) = 0.1 Section 33 331. < < < < = x x x x x x F 3 , 1 3 2 , 488 . 2 1 , 104 . 1 , 008 . , ) ( where , 512 . ) 8 . ( ) 3 ( , 384 . ) 8 . )( 8 . )( 2 . ( 3 ) 2 ( , 096 . ) 8 . )( 2 . )( 2 . ( 3 ) 1 ( , 008 . 2 . ) ( . 3 3 = = = = = = = = f f f f 337. 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 31 341. Determine E(X) and V(X) for random variable in exercise 315 . ) 8 / 1 ( 2 ) 8 / 2 ( 1 ) 8 / 2 ( ) 8 / 2 ( 1 ) 8 / 1 ( 2 ) 2 ( 2 ) 1 ( 1 ) ( ) 1 ( 1 ) 2 ( 2 ) ( = + + + = + + + = = 5 . 1 ) 8 / 1 ( 4 ) 8 / 2 ( 1 ) 8 / 2 ( ) 8 / 2 ( 1 ) 8 / 1 ( 4 ) 2 ( 2 ) 1 ( 1 ) ( ) 1 ( 1 ) 2 ( 2 ) ( 2 2 2 2 2 2 2 = + + +...
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This note was uploaded on 11/05/2008 for the course EGN 3443 taught by Professor Unknown during the Fall '08 term at University of South Florida  Tampa.
 Fall '08
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