Consider a sequence of independent random variables (left{X_{n}ight}_{n=1}^{infty}) where (X_{n}) has a (operatorname{Binomial}(1, theta)) distribution. Prove that

Question:

Consider a sequence of independent random variables $\left\{X_{n}ight\}_{n=1}^{\infty}$ where $X_{n}$ has a $\operatorname{Binomial}(1, \theta)$ distribution. Prove that the estimator

\[\hat{\theta}_{n}=n^{-1} \sum_{k=1}^{n} X_{k}\]

is a consistent estimator of $\theta$.

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

See More Books

Question Posted: Mar 15, 2024 02:00 AM

See More Questions

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...
Q1. You have identified a market opportunity for home media players that would cater for older members of the population. Many older people have difficulty in understanding the operating principles...
Consider a sequence of independent random variables Xi, each with a standard normal distribution. (a) What is P(|Xi| 0.5)? (b) If is the average of eight of these random variables, what is P(|| ...
Q4 11 Points 4. Consider the following Current Data for ABC Corp.: Debt Equity Market Value (in millions of $) 16,000 26,000 Cost 7% 14% If ABC moves to and maintains a debt-to-value (D/V) ratio of...
Blood flows through a major artery at 1.0 m/s for 0.50 s, then at 0.60 m/s for another 0.50 s through a smaller artery. (a) Is the average speed of the blood 0.80 m/s, greater than 0.80 m/s, or less...
How is an operating lease treated for tax purposes?
Assume there is a risk-free asset and a representative investor with power utility, so (7.15) is an SDF. Let z = log(c1/c0) and assume z is normally distributed with mean and variance 2. Let denote...
An auto-repair shop faces the following weekly costs: rent, $500; labor, $400 per worker; parts and supplies, $30 per repair. Each worker can repair three cars per week. a. Fill in the costs in Table...
William's Co. is considering spending $15,000 at Time 0 to test a new product. Depending on the test results, the firm may decide to spend $58,000 at Time 1 to start production of the product. If the...
Let $U$ be a $\operatorname{Uniform}(0,1)$ random variable and define a sequence of random variables $\left\{X_{n}ight\}_{n=1}^{\infty}$ as $X_{n}=\delta\left\{U ;\left(0, n^{-1}ight)ight\}$....
Let $Z$ be a $\mathrm{N}(0,1)$ random variable and let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of random variables such that $X_{n}=Y_{n}+Z$ where $Y_{n}$ is a...
Shalie Manufacturing makes several thousand different metal products, including building materials, tools, and furniture parts. The manager of the furniture parts division has proposed that his...
Draw a bar graph for each data set in Problems 32-35. Data set $\mathrm{D}$ Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 35 25 25 16 14 1...
Draw a line graph for each data set in Problems 36-39. Data set A Data set A: The annual wages of employees at a small accounting firm are given in thousands of dollars. 25 16 25 25 14 18 1 2 2 2...
For each of the angles shown: (i) Estimate its size (ii) Measure it and check how good your estimate was. Aim for your estimate to be within 10 of the actual angle. a. b. c. d. e. f.
For the quasispin model of Problem 31.1 , find the eigenvalues of $s_{0}^{(m)}$ for the levels labeled by $m$. Show that the system has a total quasispin $S$ that is the vector sum of quasispins for...
A sole proprietorship was started on January 1, 2005, when it received $$60,000$ cash from Mark Pruitt, the owner. During 2005, the company earned $$40,000$ in cash revenues and paid $$19,300$...
Use the same information from E10- 9 now assuming that All- Kinds- of- Cases Company is an IFRS reporter. In the 10-9 Required a. Conduct a lower- of- cost- or- market test for All- Kinds-of-Cases,...
Listed below are common types of current liabilities, contingencies, and commitments: a. Accounts payable b. Bank loans and commercial paper c. Notes payable d. Dividends payable e. Sales and excise...
According to the 2019 National Coffee Drinking Study from the National Coffee Association, 63% of 2,815 U.S. adults respondents reported drinking coffee in the past 24 hours. Based on these data, a...
Based on a 2018 General Social Survey poll, a 95% confidence interval for the proportion of all U.S. adults that were born in the United States is 0.8580 to 0.8850. a. What proportion of the sample...
Suppose a 95% confidence interval for a population proportion is (0.30, 0.60). Rewrite this interval in the form of p margin of error.
Required information Skip to question [ The following information applies to the questions displayed below. ] Forten Company's current year income statement, comparative balance sheets, and...
Give a breakdown of all the intangible assets with the values shown in the statement of financial position of Unilever in 2022.
1-The yield to maturity will be greater than the coupon rate when a bond is selling at a premium. Select one: a. False b. True 2-Which one of the following would have the greatest present value,...

Consider a sequence of independent random variables (left{X_{n}ight}_{n=1}^{infty}) where (X_{n}) has a (operatorname{Binomial}(1, theta)) distribution. Prove that

Question:

Step by Step Answer:

Introduction To Statistical Limit Theory

Students also viewed these Business questions