Definition 1. A standard (one-dimensional) Wiener process (also called Brownian motion) is a stochastic process {Wt }t≥0+ indexed by nonnegative real numbers t with the following properties: (1) (2) (3) (4) W0 = 0. With probability 1‚ the function t → Wt is continuous in t. The process {Wt }t≥0 has stationary‚ independent increments. The increment Wt+s − Ws has the N ORMAL(0‚ t) distribution. A Wiener process with initial value W0 = x is gotten by adding x to a standard Wiener process
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AMA470 Midterm exam March 5‚ 2010 Please show full working out in order to obtain full marks. 1. Suppose that: • The number of claims per exposure period follows a Poisson distribution with mean λ = 110. • The size of each claim follows a lognormal distribution with parameters µ and σ 2 = 4. • The number of claims and claim sizes are independent. (a) Give two conditions for full credibility that can be completely determined by the information above. Make sure to define all terms in your definition
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b. Each student must be a member of a group of 4 or 5 students‚ selected by lecturer. c. Solutions from each group must be submitted by 19 April 2013. SPECIAL DISTRIBUTIONS I. Concept of probability (3%) 1. Explain why the distribution B(n‚p) can be approximated by Poisson distribution with parameter if n tends to infinity‚ p 0‚ and = np can be considered constant. 2. Show that – and + are the turning points in the graph of the p.d.f. of normal distribution with
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was found that their mean height was 63.4 inches. Form previous studies‚ it is assumed that the standard deviation‚ σ‚ is 2.4. Construct the 95% confidence interval for the population mean. A. (61.9‚ 64.9) B. (58.1‚ 67.3) C. (59.7‚ 66.5) D. (60.8‚ 65.4) 3. Suppose a 95% confidence interval for µ turns out to be (120‚ 310). To make more useful inferences from the data‚ it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced
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The majority of Australia’s population is distributed along the coastline. The current population of around 20 million is concentrated mainly in the large coastal cities of Sydney‚ Melbourne‚ Brisbane‚ Perth and Adelaide. Brisbane and Sydney are located on the south-eastern coast consecutively. From the bottom right to the bottom left of the continent‚ located on the south-eastern to south-western coasts are Melbourne‚ Adelaide and Perth‚ respectively. These concentrated cities then branch
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Chapter 10 Statistical Inference About Means and Proportions with Two Populations Case Problem: Par‚ Inc. This case can provide discussion and differing opinions as to what hypothesis test should be conducted. Students should begin to see that logical arguments exist for structuring the hypotheses differently. In some interpretations of the problem‚ a two - tailed test can be
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Stock Returns for Normal Distributions July11‚ 2012 Part A. A1 (CRSP 2000-2008) | VW Daily | EW Daily | VW Monthly | EW Monthly | Mean | 0.00% | 0.05% | -0.12% | 0.50% | σ | 1.35% | 1.12% | 4.66% | 6.14% | Table A1 shows return means and standard deviations for the CRSP market portfolio from 2000-2008. In comparing daily vs monthly returns in both cases‚ equally weighted (EW) and value weighted (VW)‚ Table A1 shows the mean and standard deviation are bigger for
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Century National Bank The following case will appear in subsequent review sections. Assume that you work in the Planning Department of the Century National Bank and report to Ms. Lamberg. You will need to do some data analysis and prepare a short written report. Remember‚ Mr. Selig is the president of the bank‚ so you will want to ensure that your report is complete and accurate. A copy of data appears in Appendix N. (EXCEL) Century National Bank has offices in several cities in the Midwest
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(hypertension‚ diabetes‚ cholesterol in subjects‚ including medication‚ weight‚ age‚ etc) in Docsharing and using Excel‚ provide the following for the variable(s) of your choice: 1. Frequency distribution of a variable and bar graph of the same variable 2. Descriptive statistics of a continuous dataset: mean‚ median‚ mode‚ skewness‚ kurtosis‚ standard deviation 3. Cross tabulation of two variables 4. Comparison of the effect of three or more groups (single variable) on a single continuous
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1. The distribution of Intelligence Quotient (I.Q.) scores measured for 100 students in a test is as follows: I.Q.* 40-50 50-60 60-70 70-80 80-90 90-100 Number of Students 10 20 20 15 15 20 * The data is recorded with origin as 40‚ i.e. students with I.Q. between 80 and 90 are included in the first interval. The intervals included the upper class value but not the lower. Find: Arithmetic
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