A flow of claims arriving at an insurance company is represented by a homogeneous Poisson process Nt in continuous time. (Fornow, we just count the number of claims arrived by time t.) Suppose that the mean inter-arrival time is equal to 1/A, where A is apositive parameter. Let the unit of time be an hour.Question 19Suppose now that the sizes of claims are independent, and the size of a particular claim equals either 2 or 5 units of money withprobabilities 2/3 and 1/3, respectively. Denote by Kt1 and Kt2 the numbers of claims by time t, amounting to 2 or 5, respectively.That is, for example, K₁₁ is the number of claims by time t that exactly equal to 2.) What is E(K+1) ?2λt33Xt2λt4Xt3Question 20What is E(K+2) ?Xt35Xt32λt35Xt

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Answered: A flow of claims arriving at an…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A club recruit member either through active recruitment by its current members or through advertising in neighborhood billboards. Suppose that each member of the club recruit new members at a rate of 3 members per week and that advertising in neighborhood billboards generate new members at a rate of 2 members per week. Suppose further that each member is expected to stay a club member for 1 week, on average. Assume that the number of members of the club at any given time follows a birth and death process. Given that the club started with 5 members, what is the expected number of club members after the first two weeks? (Hint: refer to the theorem below) Theorem For a linear growth process with immigration and Xo = i, we have 0 · (e(x-μ)t - 1) + ie(x-μ)t, x‡μ E (X₂) = x-fl Ot + i, λ = μ.
Researchers have created every possible "knockout" line in yeast. Each line has exactly one gene deleted and all the other genes present (Steinmetz et al. 2002). The growth rate—how fast the number of cells increases per hour—of each of these yeast lines has also been measured, expressed as a multiple of the growth rate of the wild type that has all the genes present. In other words, a growth rate greater than 11 means that a given knockout line grows faster than the wild type, whereas a growth rate less than 11 means it grows more slowly. The growth rate of a random sample of knockout lines is 0.86, 1.02, 1.02, 1.01, 1.02, 1, 0.99, 1.01, 0.91, 0.83, 1.01 What is the standard deviation and variance of growth rate for this sample?
An article in Quality Engineering presents viscosity data from a batch chemical process. A sample of these data is in the table. Reading left to right and up to down, draw a time series plot of all the data and comment on any features of the data that are revealed by this plot. Consider that the first 40 observations (the first 4 columns) were generated from a specific process, whereas the last 40 observations were generated from a different process. Does the plot indicate that the two processes generate similar results? Calculate the sample mean and sample variance of the first 40 and the second 40 observations.
QUESTION 6 As the Operation manager at Giant Wholesale, you want to improve the inventory for the finished goods. The company is always having a shortage problem in product A. To analyse this product A inventory, you have collected the data as below: i)Average demand per day = 80 units ii)Working days per year = 300 days iii)Ordering cost = RM40 per order iv)Annual carrying (holding) cost rate = 10% of item cost v)Cost of product A per unit = RM150 vi)Lead time = 5 days vii) Standard deviation of daily demand= 5 units viii) Customer service level = 95% Based on the data given above, answer the following questions: a) Compute EOQ. b) Compute the annual total inventory cost. c) Based on a continuous review system (Q System), determine the optimal order quantity Q, and reorder point (R). d) Based on the periodic review system (P System), determine the period review interval (P) and target inventory level (T).
The production of jute goods (in tons) in different days of first and second half of 10 the year are shown below: Class 2-2.5 2.5-3.0 3.0-3.5 3.5-4.0 4.0-4.5 interval of production No. of 12 48 70 35 15 days in the first half of the year No. of 5 38 80 50 days in the second half of the year In which part of the year the production level is homogeneous?
What scale should we use for the regressors? Expalain the reason?
Consider a two component parallel system in which both components have times to failure and times to 0.0024 f/hr and µ1 = = 0.001 f /hr, 12 repair that are exponentially distributed. The data is 1, 0.003 r/hr and µ2 = 0.005 r/hr. Evaluate the reliability or probability of success for a mission of 1000 hr. (hint: form a history for each component using the data for failure rate and repair rate)
I would like all parts for E, ( i, ii, iii, iv v, vi) to be answered please Car tyres come in many different brands. Even on a car, the tyres can wear out after travelling differentdistances, due to cornering, braking and wheel alignment. Manufacturers of car tyresare interested in the average distance in kilometres travelled by tyres, or the lifetime of tyres until they are considered un-usable and need tobe replaced. At this time a tyre is considered unroadworthy. E) The lifetime T in thousands of km of brand E of car tyres, satisfies a probability density function given by. f(t)=(at^2 0=t=50, b(100-t) 50=t=100, 0 elsewhere) i) Show that a = 3/312500 and b= 3/6250 ii) For 36 tyres of brand E, find the expected number that will last longer than 40,000 km. iii)Sketch the graph of T on the axes below, clearly labelling the scale. iv) Find the expected value and variance of brand E car tyres. v) Find the probability that the lifetime of brand E car tyres lies within two standard…
A researcher is interested in finding out how the past average daily values of the stock prices of a firm A determine the current average daily value of its stock price. Let pt ( measured in dollars) denote the average daily value of the stock price of firm A at time t. The researcher collects data on the average daily values of the stock prices of the last quarter of 2017, i.e., t = 1,2, dots,90 and estimates the following autoregressive model with 1 lag of pt: hat(p)t = 2.48 +.05pt.1bar (R)² = 0.512, SER = 13.14. (1.13) (0.64) The standard errors are given in parentheses. Suppose that the actual average daily value of the stock price on January 2, 2018 was $506.12 and the average daily value of the stock price on December 31, 2017 was $445.12. The forecast error in the estimation of the average daily value of the stock price on January 2, 2018 will be $ (Round your answer to two decimal places.) This is all the info in the question
Suppose Aaron recently purchased an electric car. The person who sold him his new car told him that he could consistently travel 200 mi before having to recharge the car's battery. Aaron began to believe that the car did not travel as far as the company claimed, and he decided to test this hypothesis formally. Aaron drove his car only to work and he recorded the number of miles that his new car traveled before he had to recharge its battery a total of 21 separate times. The table shows the summary of his results. Assume his investigation satisfies all conditions for a one-sample t-test. Mean miles traveled Sample size t-statistic P-value п P 185 21 -0.65 0.262 The results statistically significant at a = 0.05 because P 0.05. are are not >
Question 5. A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400 students in his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each students is randomly assigned one of the examination times based on the flip of a coin. Let Y, denote the number of points scored on the exam by the ith student (0 ≤ Y ≤ 100), let X, denote the amount of time that the student has to complete the exam (X, = 90 or 120), and consider the regression model Yi = Bo + BiXitu. (1) Explain what the term u, represents. Why will different students have different values of ui? (2) Explain why E(u₁|X₁) = 0 for this regression model. (3) The Least Squares Assumptions Yi Bo + B₁Xi + Ui, i = 1,..., n, where I The error term u, has conditional mean zero given X₂: E(ui Xi) = 0; II (X₁, Yi), i 1,, n, are independent and identically distributed (i.i.d.) draws from their joint…

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