Question: Given that E{X) = X and var {X) = X for the Poisson distribution, show that sample means based on samples of N independent observations

Given that E{X) = X and var {X) = X for the Poisson distribution, show that sample means based on samples of N independent observations from a Poisson process are

(a) unbiased estimators of X

(b) distributed with variance \/N

(c) consistent estimators of X

(d) relatively more efficient as estimators of X than are means based on samples of size N — 1.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics Informed Decisions Using Data Questions!

A large national survey conducted in 1995 indicated that 18% of American adults had ever been tested for HIV at some point in their life. Suppose that in 2016 we take a simple random sample of 100...

Unit II Continuous Probability Distributions: The Normal Distribution Normal Dist1 Towards the Meaning of Continuous Probability Distribution Functions: When we introduced probabilities, we spoke of...

Possible Multiple Choice Questions for the Exam. Focus on the topics discussed in class. Chapter 1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____...

Exam 2 Statistical Analysis Part 1 of 1 - Question 1 of 20 5.0/ 100.0 Points 0.0/ 5.0 Points The stacked bar chart below shows the percentages of death due to cancer in four geographic regions of the...

cc170785fa926b2240534b10e7743155388d392a ID hours 1 37.09953814 2 34.58422938 3 37.85777106 4 36.03408777 5 38.71008438 6 38.18084857 7 37.7883698 8 38.41027533 9 39.53619743 10 37.46797595 11...

28) Statistical inference is the process by which ____ population characteristics are known with certainty. sample data are summarized using graphs and pictures population data are used to draw...

STAT_12A_Practice Score: 3.6/12 3/6 answered Question 1 Questions 1-3: It is a safety hazard for planes to fly if the payload (people, luggage, and fuel) weighs too much. Suppose that a small airline...

Find the solutions please for me. A certain brand of copper wire has flaws about every 40 centimeters. Model the locations of the flaws as a Poisson process. What is the probability of two flaws in 1...

Case Study 2: UFE Clubs Case Study, (10 marks) UFE Clubs produces ball bearings. The diameter of the ball bearings is very important for the quality purposes. The following tables shows the diameters...

Inferring Income Statement Values Supply the missing dollar amounts for the 2012 income statement of BGT Company for each of the following independent cases. Case A Case C Case B Case D Case E $770...

Which tissue contains an extensive extracellular matrix? Question 98 . All cells in free surface have cilia. Question 99 1 out What type of epithelium is found in the urinary bladder and allows it to...

Select from the foliowirg chokces lo explain what would happen if a oell oontaining 9 7 8 witer, were placed into a fols talt solutiont: a . waber would flow from the cell into the solution b . water...

A friend taking calculus is puzzled. She remembers that for a function of one variable, if the first derivative is zero at a point and the second derivative is positive, then there must be a relative...

The American Society for Microbiology (ASM) and the Soap and Detergent Association (SDA) jointly commissioned two separate studies during 2007, both of which were conducted by Harris Interactive. In...

Why do polling companies often survey 1060 individuals when they wish to estimate a population proportion with a margin of error of 3% with 95% condence?

Katrina wants to estimate the proportion of adultAmericans who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adult Americans and constructs a 95% condence...

On January 1, Year 1, a company had the following balances: Cash, $27,000; Supplies, $9,500; Land, $75,000; Deferred Revenue. $6,500; Common Stock $65,000; and Retained Earnings, $40,000. During Year...

2 (1 point) As a result of a stock dividend, total shareholders' equity remains the same. total shareholders' equity increases. total shareholders' equity decreases. retained earnings remain unchanged

BMW's M Series sports car has seen its market share fall after the release of the new MS Series a few months ago, which stage in the Product Life Cycle (PLC. is this product in? a) Maturity Ob)...