MATH 226 - 10.10.07

MATH 226 - 10.10.07 - o A X = number of times you drill...

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MATH 226 – October 10, 2007 Random Variable in example 18 of worksheet o X = number of sprinklers out of the full 10 that do work X ~ binomial(10, 0.9) o P(x ≥ 8) = P(x=8) + P(x=9) + P(x=10) = Σ 10 x=8 (10 choose x)(0.9) x (0.1) 10-x = 0.929809 On the calculator F3, sum, (nCr(10,x)*(.9)^x*(.1)^10-x) F Negative binomial distribution o Binomial experiment Y = the number of trials it takes until the r-th success occurs Y ~ neg. bino(p, r) F(y) = (y-1 choose r-1)p r (1-p) y-r Ey = r/p, var y = r(1-p)/p 2 For r = 1 we have a geometric distribution Example 21 from worksheet
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Unformatted text preview: o A X = number of times you drill until first success R = 1 0.66 P(x 3) = P(x=1) + P(x=2) + P(x=3) o B Negative binomial 0.62 y = number of times you drill until 3 rd success r = 3 P(y 10) = 10 y=3 (y-1 choose 2)(.3) 3 (.7) y-3 o C Ey = r/p = 3/.3 = 10 Var y = sqrt(3(.7)/(.3) 2 ) = 4.8 Z ~ Poisson() o F(z) = (e- z )/z! o Ez = o Z = number of defects on the dirt o P(z 12) = 12 z=0 ((e-10 10 z )/z!) o NOTE P(z 5) = 1 P(z < 5) = 1 P(z 4)...
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