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# 400Hw04ans - STAT 400 Spring 2011 Homework#4(10 points(due...

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STAT 400 Spring 2011 Homework #4 (10 points) (due Thursday, February 17, by 4:30 p.m.) No credit will be given without supporting work. 1. Suppose that the probability that a duck hunter will successfully hit a duck is 0.40 on any given shot. Suppose also that the outcome of each shot is independent from the others. a) What is the probability that the first successful hit will be on the fourth shot? Miss Miss Miss Hit 0.60 × 0.60 × 0.60 × 0.40 = 0.0864 . Geometric distribution, p = 0.40. b) What is the probability that the third successful hit will be on the ninth shot? [ 8 shots: 2 S’s & 6 F’s ] S ( ) ( ) 60 0 40 0 2 8 6 2 . . 0.40 0.0836 . OR S S F F F F F F S F S S F F F F F S F F S F S F F F S F F F S F F F S S S F S F F F F F S F S F S F F F F S F F S F F S F F S F F F F S S F F S S F F S F F F F S F S F F S F F F S F F S F F F S F S F F F F S F S F S S F F F S F F F S F S F F F S F F S F F S F F F F S S F F F F S F F S S S F F F F S F F S F S F F F F S F S F F F S S F F F S F F F F F S S F S S F F F F F S F S F S F F F F F S S F F F S F S F F S F F F F F S F S S S F F F F F F S S F F S S F F F F S F F F S F F S F S F F F F F F S S S 28 (0.40) 3 (0.60) 6 0.0836 . Negative Binomial distribution, p = 0.40, r = 3.

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c) What is the probability that the hunter would have three successful hits in nine shots? Let X = the number of successful hits in 9 shots. Then X has Binomial distribution, n = 9, p = 0.40. Need P ( X = 3 ) = ? . 1 P ) ( ) ( k n k p p k n k X - - = = P ( X = 3 ) = 6 3 ) 60 . 0 ( ) 40 . 0 ( 3 9 = 0.2508 . OR S S F F F F F F S F S S F F F F F S F F S F S F F F S F F F S F F F S S S F S F F F F F S F S F S F F F F S F F S F F S F F S F F F F S S F F S S F F S F F F F S F S F F S F F F S F F S F F F S F S F F F F S F S F S S F F F S F F F S F S F F F S F F S F F S F F F F S S F F F F S F F S S S F F F F S F F S F S F F F F S F S F F F S S F F F S F F F F F S S F S S F F F F F S F S F S F F F F F S S F F F S F S F F S F F F F F S F S S S F F F F F F S S F F S S F F F F S F F F S F F S F S F F F F F F S S S S S S F F F F F F S F F S F F F S F F S F S F F S F F F F S F S F F S F S S F S F F F F F S F F F S S F F F F S F S F F F S F F F S F F S S F F S S F F S F F F F S F F F S F S F F F S F F S S F F F F F S F F S F S F S S F F F S F F F S F F F S F F S F F S F F S F S F F F F S F F F S S F S S F F F F S F F S F F F F S S F F F S F F S F F S F
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400Hw04ans - STAT 400 Spring 2011 Homework#4(10 points(due...

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