(a)(b)Describe how the two commonly used parameter estimation methods (methodof moment and percentile matching) are applied in fitting distributions to datain actuarial calculations.The following table is a frequency distribution for claim size (£'000).Claim size: 0-11-22-44-88-1616-32No of claims: 2361257648123(i)(ii)Estimate parameters for fitting a Log Normal distribution to the abovedata by using the method of moment. Carry out a goodness of fit test andcomment on results.If the average number of claims per year is 48 then calculate the totalclaim size per year that will only be exceeded once in 1000 times. Usea skewness correction and present your results clearly.

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Answered: (a) Describe how the two commonly used…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A manufacturer makes screws with a mean diameter of 0.15 cm (centimeters) and a range of 0.10 cm to 0.20 cm; within that range, the distribution is uniform. Suppose you repeatedly draw samples of size 100 and calculate their mean. Applying the central limit theorem, what is the distribution of these sample means? a the standard deviation of the distribution is 0.01 b the standard deviation of the distribution is 0.04 c the standard deviation of the distribution is 0.03 d the standard deviation of the distribution is 0.05
It has been determined experimentally that steel wires of a certain length have strength with a mean value of 1 kip and a coefficient of variation of 16%. What is the probability that the strength of such a wire is less than 0.7 kips? Try Type I and Type III asymptotic distributions of extremes and compare the results.
It is known that 80-foot blue whales consume, on average, 3200 kg of krill per day. 100-footers consume on average 3600 kg of krill per day. Assume that the mean daily krill consumption varies linearly with whale length and that the daily consumption for a given whale follows a Gaussian distribution with a standard deviation of 200 kg of krill per day. Define the linear Gaussian distribution, P(k∣l), relating the rate of krill consumption k to whale length l.
The Project Manager found that distribution of the amount of gravel (in tons) sold by a particular construction supply company in a given week is a continuous random variable X with PDF as f(x)={█(3/2 〖(1-x〗^2) 0≤x ≤1@0 elsewhere)┤ Find the expected value and standard deviation of the amount of gravel sold in a week. [5]Consider a normally distributed random variable X with a mean of 85 and standard deviation of 10. Find P(90≤X≤100)?
In the manufacture of light emitting diode (LED), different layers of ink are on the optic lens. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X1 and X2 denote the thickness of two different layers of ink. It is known that X1 is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and X2 is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. Assume that these variables are independent. Let T as the ink total thickness. Give the estimated ink total thickness (in 2 decimal places):
In the manufacture of light emitting diode (LED), different layers of ink are on the optic lens. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X1 and X2 denote the thickness of two different layers of ink. It is known that X1 is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and X2 is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. Assume that these variables are independent. Let T as the ink total thickness. Give the estimated ink total thickness: Give the estimated standard deviation of the ink total thickness A lamp with a total ink thickness (T) exceeding 0.2405 mm lacks the uniformity of color that the customer demands. Find the probability that a randomly selected lamp fails to meet customer specifications
In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. Let X1 and X2 denote the thickness of two different layers of ink. It is known that X1 is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and X2 is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. Assume that these variables are independent. Let T as in the total thickness. a.) Find the estimated ink total thicknessb.) Find the estimated standard deviation of the ink total thickness
The return on the Tarheel Corporation stock is expected to be 12 percent with a standard deviation of 8 percent. The beta of Tarheel is 0.8. The risk-free rate is 9 percent, and the expected return on the market portfolio is 13 percent. What is the probability that an investor in Tarheel will earn a rate of return less than the required rate of return? Assume that returns are normally distributed. Round z value in intermediate calculation to two decimal places. Round your answer to the nearest whole number. %
Texas Instruments produces computer chips in production runs of 1 million at a time. It has found that the fraction of defective modules can be very different in different production runs. These differences are caused by small variations in the set-up of each production run. Managers have observed that defective rates are roughly triangular, with a lower bound of 0%, and an upper bound of 50%. Defects more likely to be near 10% than any other single value in their range. (a) Before we test any modules, let’s understand the distribution of de- fects. Simulate at least 2,000 draws from the triangular distribution and answer the following questions. 1 What is the probability of a defect rate less than 0.25 in this production run? 2 For what number M would you say that the defective rate is equally likely to be above or below M? 3 What is the probability that we will find exactly two defective modules when we test 10 modules from this production run? (b) Now suppose that we have taken a…
Weekly rates of return (on an annualized basis) for certain securities over a given period are believed to be normally distributed with a mean of 8.00% and variance of 0.25. Give two values x, and x, such that you are 95% sure that annualized weekly returns will be between the two values.
The breaking strength X(kg) of a certain plastic block is normally distributed with a mean of 1250kg and a standard deviation of 55kg. What is the maximum load such that we can expect no more than 4% of the blocks to break?
The absolute viscosity for sunflower oil is supposed to average 0.0311 Pa⋅s at 38 ∘C. Suppose a food scientist collects a random sample of 4 quantities of sunflower oil and computes the mean viscosity for his sample to be x¯=0.0318 Pa⋅s at 38 ∘C. Assume that measurement errors are normally distributed and that the population standard deviation of sunflower oil viscosity is known to be σ=0.0009 Pa⋅s. The scientist will use a one‑sample z‑test for a mean, at a significance level of α=0.01, to evaluate the null hypothesis, H0:μ=0.0311 Pa⋅s against the alternative hypothesis, H1:μ≠0.0311 Pa⋅s. Complete the scientist's analysis by calculating the value of the one-sample z‑statistic, the p‑value, and then deciding whether to reject the null hypothesis. First, compute the z‑statistic, z. Provide your answer precise to two decimal places. Avoid rounding within calculations. z= Determine the P-value of the test using either a table of standard normal critical values or…

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