Poisson distribution-plausible model

Assignment Help Basic Statistics
Reference no: EM1311714

Let X be a Poisson random variable with probability density function:

p (x) = λe/x!   When x = 0, 1, 2, 3, ...

Where the parameter λ > 0,

For this random variable

Consider a random sample of size n from the X distribution, and let

Y =∑Xi, be the sample sum.

a. Show that Y/n is a maximum likelihood estimator of λ. 

b. Show that the estimator in part (a) is unbiased and consistent.

c. Also, show that Y/n is an efficient estimator of λ.

d. In 1980, asbestos fibers on filters were counted as part of a project to develop measurement standards for asbestos concentration by the National Institute of Science and Technology.  Twenty three random samples yielded the following counts:

31, 29, 19, 18, 31,28,34,27,34,30,16,18,26,27,27,18,24,22,28,24,21,17,24

Assuming that the Poisson distribution is a plausible model in describing variability of asbestos fiber counts in filters; derive a 95% confidence interval indicating the variability in the average number in asbestos fibers.

Reference no: EM1311714

Questions Cloud

Evaluate the product cost : Calculation of product cost of providing one evening of instruction - Evaluate the product cost of providing one evening of instruction for all students?
Calculate the angular separation between these two lines : The sodium D line is a doublet consisting of two wavelengths, 588.995 and 589.592 nm. Calculate the angular separation between these two lines in the first-order spectrum for a grating with 4000 lines per centimeter. Repeat for the second order.
Comparison between experience or learning from books : A Compare and contrast paragraph on learning something from experience and learning from book Compare and contrast calling on a cell phone and a regular phone.
Marketplace demand for a type of carpet : The marketplace demand for a type of carpet produced by a monopolist known as KP-7 has been estimated
Poisson distribution-plausible model : Assuming that the Poisson distribution is a plausible model in describing variability of asbestos fiber counts in filters; derive a 95% confidence interval indicating the variability in the average number in asbestos fibers.
Present value rigorous federal drug administration testing : Computation of Present value and the process had yet to pass rigorous Federal Drug Administration testing and was still in the early stages of development
Mcq on utility maximization and market structure : Joan is deciding where to spend her spring break.  If she goes to Cancun, Mexico, the trip will give her 9,000 utils of satisfaction and will cost her $300.  If, instead, she travels to Florida, the trip will give her 5,000 utils of pleasure and w..
Balance sheet would a bank rather have primarily : If a deposit outflow of $50 million occurs, which balance sheet would a bank rather have primarily or the following balance sheet.
How long will it take the bullet to come to a stop : Smoke particles in the air typically have masses of the order of 10 to 16 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with microscope.

Reviews

Write a Review

 

Basic Statistics Questions & Answers

  Evaluate the p-value of the anova f test

The hypotheses tested by the one-way ANOVA F test - Evaluate the P-value of the ANOVA F test

  Evaluate the sum of the ranks for neighborhood

Real estate agents always say "location, location, location" is the most important thing in buying a house. We want to know if the sales prices of homes in two neighborhoods are similar. A random sample is taken from each neighborhood. The prices ..

  Strength of a relationship

Which of the following measures only the strength of a relationship?

  Statistics-probability assignment

MATH1550H: Assignment:  Question:  A word is selected at random from the following poem of Persian poet and mathematician Omar Khayyam (1048-1131), translated by English poet Edward Fitzgerald (1808-1883). Find the expected value of the length of th..

  What will be the standard deviation of the number of men

what is the chance the average contents of the cans will be less than advertised and what will be the standard deviation of the number of men who help at home, based on the first survey

  Test of the hypotheses

The alternative hypothesis is true. In this case the consumer advocacy group will have, A consumer advocacy group doubts this claim and tests the hypotheses

  Probability that person will fall in book keeping category

One person's file is chosen at random. Find out probability that selected person will fall into following categories. Book keeping.

  A partial anova table

Their resting heart rates were measured. A partial ANOVA table is given.

  Questions based on binomial distribution

Questions based on binomial distribution, variance of the binomial distribution, discrete random variable and continuous random variables.

  Determine if there are patterns of either excellence or lack

These can have a large impact on tenure and promotion decisions at many institutions. One particular instructor had ratings in 3 courses in one semester as given by the table below for the statement "The instructor is an excellent teacher.

  What is the sample space for this process

What is the sample space for this process and evaluate the variance of the intelligence scores

  Correct conclusions from this procedure

Multiple comparison procedures are going to be done using the Bonferroni method with α = 0.10. The value of t** is 2.2426. The smallest minimum significant difference (MSD) for finding a difference between groups is computed as 17.68. The correct ..

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd