S490C F07 Final Solutions - STAT 490C FINAL December 12,...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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 ct = 3 and 0 = 2000 0.5x 0§X<l.2 ii. (2 points) F(X) = 0.6 1.2 _<_ X < 2.4 0.5X- 0.6 2.4gx<3.2 iii. (2 points) F(X) = 0.1x -1 10 f X <15 0.05x 15 5 X < 20 SEE MW at W” 2. (7 points) You are given the following random sample of 3 data points from a population with a Pareto distribution with G = 70: X: 15 27 43 Calculate the maximum likelihood estimate for CL. 555. #W Hg (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 l 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 )b estimated by the maximum likelihood estimator. Calculate the 95% confidence interval for X. ,‘ . ("a $5755 “t” “A w W? W (1110313 +(Joe)(> «if r 9K” W X W Mia) May it) if” 5‘”) bi +67%) waxagwm \ M waved/mama»: we“; fl " ”' flfly. T grit} (:39 {a g as 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 2 l 30 I 3 l 10 4+ 5 You are given the following hypothesis: H0: The distribution of the number of accidents per day is distributed as Poison with a mean of 0.625. H1: The distribution of the number of accidents per day is not distributed as Poison With a mean of 0.625. (6 points) Calculate the chi—square statistic. (2 points) Calculate the critical value at a 10% significance level. (1 point) State Whether you would reject the H0 at a 10% significance level. 5,556“ HW #/‘f/ Based on a random sample, you are testing the following hypothesis: Ho: The data is from a population distributed binomial with m = 6 and q = 0.3. H1: The data is from a population distributed binomial. You are also given: L(60) = .1 and L(01) = .3 (2 points) Calculate the test statistic for the Likelihood Ratio Test (2 points) State the critical value at the 10% significance level §>EE 44- /‘/3 (4 points) You are given the following 9 claims: X: 10, 60, 80, 120, 150, 170, 190, 230, 250 The sum ofX : 1260 and the sum of X2 = 227,400. The data is modeled using an exponential distribution With parameters estimated using the percentile matching method. Calculate 9 based on the empirical value of 120. 5% WM #5 (7 points) Craig has an automobile insurance policy. The policy has a deductible of 500 for each claim. The number of claims follows a Poison distribution with a mean of 2. Automobile claims are distributed exponentially with a mean of 1000. The insurance company uses simulation to estimate the claims. A random number is first used to calculate the number of claims. Each claim is then estimated using random numbers and the inverse transformation method. The random numbers generated from a uniform distribution on (0, l) are 0.7, 0.1, 0.5, 0.8, 0.3, 0.7, 0.2. Calculate the simulated amount that Craig would have to pay in the first year. (4 points) A sample of two selected from a uniform distribution over (0,U) produces the following values: 3 7 You estimate U as the MaX(X1, X2). Estimate the Mean Square Error of your estimate of U using the bootstrap method. £56 #142 if /5/ 9. Schmidt’s Bakery has workers’ compensation claims during a month of: 100, 350, 550, 1000 Schmidt’s owner, a retired actuary, believes that the claims are distributed exponentially with 0 = 500. He decides to test his hypothesis at a 10% significance level. (5 points) Calculate the Kolmogorov-Smirnov test statistic. éflg 717‘: JEE (2 point) State the critical value for his test. (1 point) State his conclusion. (1 points) He also tests his hypothesis using the Anderson-Darling test statistic. State the values of this test statistic under Which Mr. Schmidt would reject his hypothesis. 10. (6 points) The following sample is from a population with an exponential distribution: X: 300, 400, 500 The parameter 6 is estimated using the maximum likelihood estimator. Use the delta method to estimate the mean and variance of p = Pr(x>300). 11. (4 points) You are given the information matrix for the estimation of (X and 9 is: 2.00 -0.40 -0.40 1.08 Calculate the Var(0c), the Var(9), and COV(0L,9) 7— Q/QzéD 0 //,//_fs yMA 12. (6 points) You are given the following sample of claims obtained from an inverse gamma distribution: X: 12, 13, 16, 16, 22, 24, 26, 26, 28, 30 The sum ofX is 213 and the sum osz is 4921. Calculate 0L and 9 using the method of moments. Eé 50/ Mg) 13. (3 points) State whether the following are true or false i. The principle of parsimony states that a more complex model is better because it will always match the data better. ii. In judgment-based approaches to determining a model, a modeler’s experience is critical. iii. In most cases, judgment is required in using a score—based approach to selecting a model. £55 AW #M/ ...
View Full Document

This note was uploaded on 03/15/2012 for the course STAT 490 taught by Professor Na during the Fall '11 term at Purdue University-West Lafayette.

Page1 / 13

S490C F07 Final Solutions - STAT 490C FINAL December 12,...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online