proj1 - STA 4322/5328 Project 1 Spring 2010 Due Thursday...

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STA 4322/5328 – Project 1 – Spring 2010 Due Thursday Feb. 4 Part 1: Customers arriving at a Restaurant The number of customers arriving at Cow-Fil-A between 11:30 and 1:30 on weekdays follows a Poisson distribution with mean λ =25 per 10 minute period. The manager observes the number of arrivals in each 10 minute period (and treats them as independent observations). Thus on a given day, she observes: 12 1 ,..., Y Y ~ Poisson( λ =25) and each day she computes: ( 29 = = - - = = n i i i i Y Y n S Y Y 1 2 2 12 1 1 1 and 12 1 1. Give the mean and variance of Y 2. Give the theoretical mean and variance of Y 3. If 12 1 ,..., Y Y ~N( μ,σ 2 ), what would be the distribution of (n-1)S 2 / σ 2 ? 4. Obtain m=10,000 random samples of n=12 from the Poisson ( λ =25) distribution, and obtain the sample mean and variance of each sample. a. Give histograms of the sample means and variances b. Give the empirical mean and variance for the sample mean and variance: ( 29 ( 29 = = = = - = = - = = 10000 1 2 2 2 2 10000 1 2 2 10000 1 2 2 10000 1 10000 1 10000 1 10000 1 10000 1 2 j j s j j j j Y j j S S S S S Y Y S Y Y c.
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