Consider an auto insurance portfolio where the number of accidents follows a Poisson distributionwith parameter λ= 1000. Suppose the damage sizes for separate accidents are i.i.d. (independentidentically distributed) r.v.'s having an exponential distribution with a mean of $2500.Each policy involves a deductible of $500. Let N₁ be the number of accidents that result in claims,and N₂ be the number of accidents that do not result in claims.Answer the following questions 1-5.Q1Are N₁, N₂ dependent?Q2Depends on a situation,NoYesWhat is the name of the distributions of N₁, №₂?O Marked PoissonGammaExponentialCompound Poisson Q3What is the mean and variance of N₁? The numbers below are rounded.Q4181.27, 32858.811000, 10001000, 1000000818.73, 818.73818.73, 670318.81What is the mean and variance for N₂? The numbers below are rounded.181.27, 181.271000, 10000001000, 1000818.73, 818.73818.73, 670318.81

Yes, . has Poisson distribution and has exponential distribution.

Answered: Consider an auto insurance portfolio…

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 water park has an 18-minute ride through man-made rapids and waterfalls. When the ride is in full operation, riding times for passengers are uniformly distributed between 0 and 18 minutes. Suppose an electrical problem leads to a temporary stoppage. What percent of the riders had been on the ride for less than 2 minutes when the stoppage occured? And what percent of the riders had been on the ride between 10 and 15 minutes when the stoppage occured?
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1.(i) Test the claim that p is more than 0.301. Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: p > 0.301; H1: p = 0.301 H0: p = 0.301; H1: p > 0.301 H0: p = 0.301; H1: p < 0.301 H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling distribution will you use? The…
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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 221 numerical entries from the file and r = 50 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. (i) Test the claim that p is less than 0.301. Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ho: P = 0.301; H₁: p = 0.301 Ho: P 0.301 Ho: P = 0.301; H₁: p 5 and nq > 5. O The Student's t, since np 5 and nq > 5. What is the value of the…
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 226 numbers from this file and r = 87 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. 1) Test the claim that p is more than 0.301. Use α = 0.10. 2) What is the value of the sample test statistic? (Round your answer to two decimal places.) 3) Find the P-value of the test statistic. (Round your answer to four decimal places.) 4) If p is in fact larger than 0.301, it would seem there are too many numbers in…
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 225 numerical entries from the file and r = 51 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.05.
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…

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