STA3007_ass5 - STA 3007 Assignment 5 Self-correction...

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STA 3007 Assignment 5: Self-correction problems Students are not required to submit. Solutions for the first three questions will be provided shortly. 1. Customers demanding service at a central processing facility arrive accord- ing to a Poisson process a intensity θ = 8 per unit time. Independently, each customer is classified as high priority with probability α = 0 . 2, or of low priority with probability 1 - α = 0 . 8. What is the probability that three high priority and five low priority customers arrive during the first unit of time? 2. Men and women enter a supermarket according to independent Poisson process having respective rates of two and four per minute. (a) Starting at an arbitrary time, what is the probability that at least two men arrive before the first woman arrives? (b) What is the probability that at least two men arrive before the third woman arrives? 3. Stocks occur to a system according to a Poisson process of intensity λ .
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