Answered: 16. Annual claim numbers Xi are modeled… | bartleby

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 31PPS

See similar textbooks

Related questions

Question

Please do the following questions with full working out

16. Annual claim numbers Xi are modeled by a Poisson distribution with
unknown parameter A. Prior knowledge about A can be summarized by
a uniform distribution on the interval [60, 120].
(a) Determine the form of the Bühlmann credibility estimator of the
pure premium E(Xn+1) based on a random sample x of claim num-
bers over n years.
(b) What would the estimate be if X = (106, 105, 110, 98, 101, 113)?

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Suppose the number X of tornadoes observed in a particular region during a one-year period has a Poisson distribution with 2 = 8. i. Compute P(X 55), ii. How many tornadoes can be expected to be observed during the 1-month period? What is the standard deviation of the number of observed tornadoes during 6 months period?
None
= 16. A simple random sample of size n = 64 is obtained from a population with u = 77 and o = (a) Describe the sampling distribution of x. (b) What is P (x>79.5) ? (c) What is P (xs72.9)? (d) What is P (75.9 79.5) = (Round to four decimal places as needed.) (c) P (xs72.9) = (Round to four decimal places as needed.) (d) P (75.9
Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 = 3.
The weights of men in a particular age group have mean u = 180 pounds and standard deviation o = 32 pounds. (a) For randomly selected samples of n = 16 men, what is the standard deviation, s.d., of the sampling distribution of possible sample means? s.d.(x) = (b) For randomly selected sanples of n = 64 men, what is the standard deviation, s.d., of the sampling distribution of possible sample means? s.d.(x) = (c) In general, how does increasing the sample size affect the standard deviation of the sampling distribution of possible sample means? Parts (a) and (b) provide a hint. Increasing the sample size decreases sample size multiplies the standard deviation by a factor of one-half v the value of the standard deviation of the sampling distribution of the sample mean. A fourfold increase in
Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 100 pounds and a standard deviation of 38.6 pounds. Random samples of size 20 are drawn from this population and the mean of each sample is determined. ux= o-x= graph=
Let Y, represent the ith normal population with unknown mean 4, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S?=₁1(Y-₁². (h) Find the standard error of U₂ in part (g), assuming that of = 0² = 0². (i) Discuss how the distribution of Y₁ - Y₂ can be used to test the equality of the two population means, #₁1 and 12, when o=o=o² is known. (i) Define appropriate rejection regions, in terms of Y₁-Y₂, for testing Ho: #₁ = 1₂ against a two-sided alternative hypothesis at the a level of significance.
Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2. Consider independent random samples, Ya,Ya. Yin, of size n,, from the ith population with sample mean Y, and sample variance S?=₁1(Yu - Y.². (g) For non-zero constants a,'s, what is the distribution of U₂ = a₁Y₁-a₂Y₂? State all the relevant parameters of the distribution. (h) Find the standard error of U₂ in part (g), assuming that of = o2 = 0². (i) Discuss how the distribution of Y₁ - ₂ can be used to test the equality of the two population means, #, and p2, when of=o=o² is known. (j) Define appropriate rejection regions, in terms of Y₁ - ₂, for testing Ho: #₁ = ₂ against a two-sided alternative hypothesis at the a level of significance.
7. (Sec. 3.6) Consider sending packets of data through the internet, and we have a counter that determines the number of missing/corrupted packets. Suppose that number X has a Poisson distribution with parameter 23. = (a) What is the probability that the counter determines that the transmission has exactly one miss- ing/corrupted packet of data? (b) What is the probability that the counter determines that the transmission has at least 3 miss ing/corrupted packets of data? (c) If two transmissions of data across the internet ar that at least one of them does not contain a missing/corrupted packet? e independently selected, what is the probability
Suppose a sample Y1, ..., exponential distribution with E (Yi) = 0 and V (Yi) = 02. Let 0^ be an estimator of the mean, 8. Yn is selected from an 1. Explain what a parameter is. What is the parameter of interest in this case? 2. Name the properties of a good estimator and explain, shortly, what is meant by each. (a) (b) (c) 3. Given the properties you discussed in (2) and the parameter of interest identified in (1), what estimator would you propose? 4. What would the sampling distribution of this estimator be? Why?
Q1: Suppose the number of customers X that enter a store between the hours 9:00 a.m. and 10:00 a.m. follows a Poisson distribution with parameter 0. Suppose a random sample of the number of customers that enter the store between 9:00 a.m. and 10:00 a.m. for 10 days results in the values 9, 7, 9, 15, 10, 13, 11, 7, 2, 12 Determine the maximum likelihood estimate of 0. Show that it is an unbiased estimator. Q2: Assume that X is a discrete random variable with pmf f(x). Let X₁,...,X₁ be a random sample on X. Suppose that the space of X is finite, say, D={a₁,...,m}. An intuitive estimate of p(a) is the relative frequency of a, in the sample. We express this more formally as follows. For j=1, 2,..., m, define the statistics 1,(X) = {1 0 X₁ = a; X₁ = a; Then the intuitive estimate of p(a)) can be expressed by the sample average p(a) = -1,(X₂) Find the unbiased estimator and the variance of the estimator and its mgf.
1. Suppose X1, X2, .,X, ~ Pois(A), i.e., is a random sample from a Poisson distribution with mean A. The MLE for A is X. (a) How would you construct an exact 95% CI for A based on this MLE? (b) Assuming n is large enough, exploit the CLT and construct an approximate 95% CI for A based on this MLE. (c) How could you study how well the approximate CI works through a simulation study? Write out the steps of the simulation study. You don't need to write any code or use R syntax.

SEE MORE QUESTIONS

Recommended textbooks for you

Glencoe Algebra 1, Student Edition, 9780079039897…

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

Glencoe Algebra 1, Student Edition, 9780079039897…

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

SEE MORE TEXTBOOKS