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stat400lec14 - with mean life of 5000 hours And Ping has...

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Statistics 400 Lecture 14 (Sep 26) Waiting Time Review: Continuous distribution Percentile : The (100p)th percentile π p is a number such that the area under f(x) to the left of π p is p. That is: first quartile : 25th percentile median : 50th percentile third quartile : 75th percentile Example: Let X have the p.d.f f(x)=e -x-1 -1<x< ∞ find median. Ping Ma Lecture 14 Fall 2005 - 1 -
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Review: Poisson distribution. Example: Customers arrive at Staples according a Poisson distribution with mean rate 1/3 per minute. Staples opens on 9:00am in the Morning. Let W denote the waiting time until the first customer comes in. What is the cumulative distribution function of W. F(w)=P(W<w) =1-P(W>w) =1-P(no customer come in between 0 and w minutes) f(w)= Exponential distribution p.d.f. θ θ / 1 ) ( x e x f - = ∞ < ≤ x θ E[X]= Var[X]= F(x)= Ping Ma Lecture 14 Fall 2005 - 2 -
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Example: Suppose that the life of Ping’s IBM laptop has an exponential distribution
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Unformatted text preview: with mean life of 5000 hours. And Ping has used his laptop for 3000 hours, what is the probability that laptop will last for another 6000 hours. Ping Ma Lecture 14 Fall 2005- 3 -Example : Customers arrive at Staples according a Poisson distribution with mean rate 1/3 per minute. On Thanksgiving morning, Staples opens 5:00am in the Morning. The first 10 customers will get a free flash drive. Let W denote the waiting time until the 10 th customer comes in. What is the cumulative distribution function of W. F(w)=P(W<w) =1-P(W>w) =1-P(fewer than 10 customers come in between 0 and w minutes) =1-∑ =-9 3 1 ! ) 3 1 ( k w K k e w Ping Ma Lecture 14 Fall 2005- 4 -Gamma function dy e y t y t ∫ ∞--= Γ 1 ) ( = Γ ) ( n Gamma distribution θ α / 1 ) ( 1 ) ( x e x x f--Γ = ∞ < ≤ x Ping Ma Lecture 14 Fall 2005- 5 -...
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