Suppose the random variable Y has a binomial distribution with parameters n and p. a. Show that

Question:

Suppose the random variable Y has a binomial distribution with parameters n and p.

a. Show that p̂ = y/n is an unbiased estimator of p.

b. Find the variance of p̂.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Statistics For Engineering And The Sciences

ISBN: 9781498728850

6th Edition

Authors: William M. Mendenhall, Terry L. Sincich

See More Books

Question Posted: May 17, 2021 07:55 AM

See More Questions

Suppose that the random variable Y has a binomial distribution with n trials and success probability X, where n is a given constant and X is a uniform(0,1) random variable. (a) Find EE and Var Y. (b)...
Suppose the random variable y has a Poisson distribution. Compute the following probabilities: a. P(y = 4) given = 2 b. P(y = 4) given = 3.5 c. P(y > 4) given = 2 d. P(1 y
Suppose that X has the binomial distribution with parameters n and p, and that Y has the negative binomial distribution with parameters r and p, where r is a positive integer. Show that Pr(X < r) =...
Over the past 10 years, a bank has experienced the following loan losses on its C&I loans, consumer loans, and total loan portfolio. Using regression analysis on these historical loan losses, the...
In Example 4.3-2, suppose that for toy trains the per-unit time of operation 2 can be reduced from 3 minutes to at most 1.25 minutes. By how much must the per-unit time of operation 1 be reduced to...
Toby would like to purchase partly paid shares in a mining company. He is confused as to the differences between mining companies whose name ends with Pty Ltd from a mining company whose name ends...
What is SS, the sum of the squared deviations, for the following population of N 5 5 scores? Scores: 1, 9, 0, 2, 3 a. 10 b. 41 c. 50 d. 95
Institute Limited organized late in 2013 and set up a single account for all intangible assets . The following summary shows the entries in 2014 (all debits) that have been recorded in intangible...
Figure 5.2, Figure 5.5 and Figure 5.6 Since the SUTA rates changes are made at the end of each year, the available 2019 rates were used for FUTA and SUTA. Note: For this textbook edition the rate...
Flosun plc makes and sells a range of products. Management has carried out an analysis of the total cost of production. The information in Appendix 3.1 reflects this analysis of budgeted costs for...
Let y 1 , y 2 , y 3 , . . . , y n be a random sample from a Poisson distribution with mean , i.e., E (y i ) = , i = 1, 2, .... n. Consider four estimators of : a. Which of the four estimators are...
Let y 1 , y 2 , . . . , y n be a random sample of n observations from an exponential distribution with mean . Derive a large-sample confidence interval for . Start with the pivotal statistic and show...
Find the circumference and area of the circle. Approximate each value to the nearest tenth when appropriate. r = 2x
The Role of Leadership in Shaping Organizational Culture Recent research stated that [c]ompanies with an established organizational culture that includes strong capabilities for change, commitment to...
Unscheduled absences by clerical and production workers are an important cost in many companies. Reducing the rate of absenteeism is, therefore, an important goal for a company's human relations...
Many of the largest tech firms, including Google, Apple, Amazon, and Microsoft, have spent hundreds of millions of dollars to improve their information technology infrastructure. Now, these companies...
In the business sense, a product refers to a commodity available for purchase, encompassing both services and tangible or intangible items. It may exist in physical, virtual, or cyber forms. Every...
Data Exploration and Multiple Linear Regression (MLR) using SAS. The "College" data set contains the statistics for many US Colleges from 1995 issue of US News and World Report. It has 777...
Explain why management accounting practices tend not to differ across countries.
7 A 29-year-old, previously healthy man suddenly collapses at a party where legal and illicit drugs are being used. Enroute to the hospital, he requires resuscitation with defibrillation to establish...
Consider the following logic variables for a car: W = the seatbelt warning light is on D = a door of the car is open Ps = there is a passenger in the passenger seat K = the key is in the ignition M =...
Consider the following logic variables for a car: M = the motor is running Db = the drivers seat belt is fastened In the early 1970s the government ordered all seat belt warnings to be tied to the...
Consider the sentence, If a customer at a restaurant is over 21 and shows proper identification, then she can order an alcoholic beverage. (a) Express this sentence as a logic equation, and (b) write...
Palisade Creek Co. is a merchandising business that uses the perpetual inventory system. The account balances for Palisade Creek Co. as of May 1, 2019 (unless otherwise indicated), are as follows:...
1-When accounting for an acquisition, goodwill is the difference between what two things? 2- What factors should be considered when deciding whether an acquisition should be financed with cash or...
What is the main friction Fluidity aims to address? REAL STATE

Suppose the random variable Y has a binomial distribution with parameters n and p. a. Show that

Question:

Step by Step Answer:

a To show that p yn is an unbiased estimator of p we need to show that Ep p Ep Eyn 1...View the full answer

Statistics For Engineering And The Sciences

Students also viewed these Engineering questions