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ST 558 Homework 4

# ST 558 Homework 4 - Kelly Harrison ST 558 D Homework 4...

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Kelly Harrison 2/14/10 ST 558 D Homework 4 PROBLEM 1 Determine the value c so each of the following functions can serve as a probability distribution of the discrete random variable x. a) f(x) = c(x 2 +4), x = 0, 1, 2, 3 f(x) = 1 c(0 2 +4) + c(1 2 +4) + c(2 2 +4) + c(3 2 +4) = 1 c[4 + 5 + 8 + 13] = 1 30c = 1 c = 1/30 b) f(x) = c(2,x)(3,3-x) for x = 0, 1, 2 f(x) = 1 c(2,0)(3,3-0) + c(2,1)(3,3-1) + c(2,2)(3,3-2) = 1 c(1)(1) + c(2)(3) + c(1)(3) = 1 c(1 + 6 + 3) = 1 10c = 1 c = 1/10 PROBLEM 2 The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function: f(x) = 20,000/(x+100) 3 , x > 0 0, elsewhere ( 29 ( 29 ( 29 ( 29 ( 29 p p 3 3 2 p p 200 200 200 2 2 2 p 20, 000 1 P(x 200) dx 20, 000 lim x 100 dx 10, 000 lim | x 100 x 100 1 1 1 10, 000 lim 10, 000 0 300 p 100 200 100 1 9 - ¬ = = + = - + + = - - = - - = + + b) ( 29 ( 29 ( 29 ( 29 ( 29 120 120 120 3 3 2 80 80 80 2 2 20, 000 1 P(80 x 120) dx 20, 000 x 100 dx 10, 000 | x 100 x 100 1 1 10, 000 .10203 120 100 80 100 - < < = = + = - + + = - - = + +

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PROBLEM 3
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ST 558 Homework 4 - Kelly Harrison ST 558 D Homework 4...

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