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S490C F07 Final

# S490C F07 Final - STAT 490C FINAL 1 A random number of 0.6...

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STAT 490C FINAL December 12, 2007 1. A random number of 0.6 is generated from a uniform distribution on (0, 1). Using the inverse transformation method, calculate the simulated value of X assuming: i. (3 points) X is distributed Pareto with α = 3 and θ = 2000 0.5x 0 < x < 1.2 ii. (2 points) F(x) = 0.6 1.2 < x < 2.4 0.5x - 0.6 2.4 < x < 3.2 iii. (2 points) F(x) = 0.1x -1 10 < x < 15 0.05x 15 < x < 20

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2. (7 points) You are given the following random sample of 3 data points from a population with a Pareto distribution with θ = 70: X: 15 27 43 Calculate the maximum likelihood estimate for α.
3. (5 points) During a one-year period, the number of accidents per day in the parking lot of the Steenman Steel Factory is distributed: Number of Accidents Days 0 220 1 100 2 30 3 10 4 2 5 0 6 1 7 1 8 1 9+ 0 The accidents are assumed to be distributed following a Poison distribution with λ estimated by the maximum likelihood estimator. Calculate the 95% confidence interval for λ.

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4. During a one-year period, the number of accidents per day in the parking lot of the Steenman Steel Factory is distributed: Number of Accidents Days 0 220 1 100 2 30 3 10 4+ 5 You are given the following hypothesis: H 0 :
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