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/λ, where X is apositive parameter. Let the unit of time be an hour.Question 17Suppose it is 10 a.m. now, and the last claim had arrived at 9:00 a.m. What is the probability that the inter-arrival time between thelast and the next claim will be not smaller than 2 hours? (In other words, after 9:00 a.m. you will wait for the next claim at least 2hours, but your present time is 10am, and you do know when the last claim arrived. )2e-1et - e-te-21e-1Question 18Suppose it is 10 a.m. now, and the last claim had arrived at 9:00 a.m.. What is the probability that there will be exactly three claimsbetween 9:30 a.m. and 1 p.m.?-4X32 1³ e27X³e-3x2/A³e-3A8373 X ³ - 7 148

Since, there are multiple questions. As per Bartelby guidelines, only one question can be solved.…

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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Suppose you have four classifications: freshmen (f), sophomore (so), junior (j), and senior (se). You construct a dummy variable, one for each classification that takes on the value of (1) should that classification be true for that observation and 0 otherwise. Further assume that you estimate the following model: E[GPA]= .5*ACT+0*So+-0.42*J+{c}*Se How much higher/lower is a Junior's GPA, after controlling for ACT, than for the omitted category?
A student is speeding down Route 11 in his fancy red Porsche when his radar system warns him of an obstacle 400 feet ahead. He immediately applies the brakes, starts to slow down, and spots a skunk in the road directly ahead of him. The "black box" in the Porsche records the car's speed every two seconds, producing the following table. The speed decreases throughout the 10 seconds it takes to stop, although not necessarily at a uniform rate.
a) Fifty parts are tested for 500 cycles each. When a part fails, it is replaced by another one. At the end of the test, 5 parts had failed. What is the failure rate? b)Determine the reliability at t = 3500 cycles for Example Problem 11-10, where the mean life of a constant failure rate is 3704 cycles. What is the reliability at t = 3650 cycles? At 3900 cycles?
5.. The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes forty percent of the time, the light will change before you have to wait how long? 36 seconds O 60 seconds 48 seconds O 72 seconds None of Above
The following table shows the hot dogs bought from a street vendor over the course of eight days ("Demand"). Also shown is the temperature for each day in degrees Celsius. Temperature (°C) 21 13 22 19 5 13 16 23 Demand 45 30 34 42 16 21 40 35 y=10.99+1.33x The predicted demand for hot dogs on a day with a temperature of 15°C is (Round to the nearest integer as needed.)
A surplus store gives a scratch‑off ticket to 2000 customers as they leave with their groceries. Can we expect these customers’ average winnings to be close to the average winnings for the entire population of the scratch‑off ticket holders? Yes No This cannot be determined from the information given.
We want to assess the relationship between class rank and how many minutes a person spends on social media. We randomly select 5 students from UMD and have them report their class rank and number of minutes per week they spend on social media. We get the following data. Because class rank is ordinal data, we want to compute Spearman's rho. Please compute the numerator for Spearman's rho and use 4 decimal places for all computations and final answer. (the numerator is referring to the numerator of the fraction, not including the 1- part) Minutes on Social Class Rank Media per Week 100 1,302 500 25 250 10 600 50 200
The production of jute goods (in tons) in different days of first and second half of the year are shown below: Class interval of production No. 2-2.5 2.5-3.0 3.0-3.5 3.5-4.0 4.0-4.5 of 12 48 70 35 15 days in the first half of the year No. of 5 38 80 50 7. days in the second half of the year In which part of the year the production level is homogeneous?
1.40 Continuous or Discrete? Identify each variable as continuous or discrete: EX a. Number of homicides in Detroit during a one-month period b. Length of time between arrivals at an outpatient clinic c. Number of typing errors on a page of manuscript d. Number of defective lightbulbs in a package containing four bulbs e. Time required to finish an examination
Question 1. A researcher wants to study the effect of a price change on the sales of various brands of a certain product. Assume the market is made up of four brands - W, X, Y and Z- and the price change (decrease) for brand W is introduced immediately after time t0. Assume every respondent buys exactly one unit of the product in each period. Data on number of respondents buying each brand in each period, based on a panel, are as follows: Y W 175 25 100 25 25 Y 25 50 50 25 Note: Confine your attention only to the data presented Assume the world starts at to and stops after ti and the strategies of brands X, Y, and Z are unchanged between to and ti. c) Which brand(s) other than W exhibited the highest loyalty rate? Show your calculations. d) Which of the brands X Y, Z should be most worried about W's promotion? Show your calculations. to
A biologist is monitoring several small groups of elk. Each group is made of one or two "resident" males, however during mating season "bachelor" males will challenge the resident males of the heard. The biologist records the following information about the encounter. Identify each of the variables below as Categorical, Quantitative Discrete, Quantitative Continuous, or Identifier. Who won the challenge - the bachelor or the resident How long the challenge lasts How many cows (females) are in the group Estimation of the general health of the group, on a scale of 1 (poor) to 5 (robust) Designation/name of the group
The percentage of employees who cease their employment during a year is referred to as employee turnover, and it is a serious issue for businesses. The following table shows the cost, in millions of dollars, to a certain company for a given employee turnover percentage in a year.

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