If 2n 1 random observations are drawn from a continuous and symmetric pdf with mean and if f Y ( ) 0, then the sample median, Y n 1 , is unbiased for , and Var(Y n 1 ) 1 (8 f Y ( ) 2 n) Show that n Y n 1 is consistent for

Question: If 2n + 1 random observations are drawn from a continuous and symmetric pdf with mean and if f Y (; ) = 0,

If 2n + 1 random observations are drawn from a continuous and symmetric pdf with mean μ and if f_Y(μ; μ) = 0, then the sample median, Yʹ_n+1, is unbiased for μ, and Var(Yʹ_n+1) = 1/(8[f_Y(μ; μ)]²n) Show that ˆμ_n = Yʹ_n+1 is consistent for μ.

Step by Step Solution

★★★★★

3.26 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Because the symmetry of the p... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

681-M-C-M-S (870).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Suppose that fY (y) is a continuous and symmetric pdf, where symmetry is the property that fY (y) = fY (y) for all y. Show that P (a Y a) =2FY (a) 1.

The following 20 observations are drawn from a censored normal distribution: The applicable model is y*i = + i, y + i = y*i if + i > 0, 0 otherwise, i ~ N [0, 2]. Exercises 1 through 4 in this...

Data with 250 observations are drawn from a bell-shaped distribution with a mean of 50 and a standard deviation of 12. Approximately how many observations are more than 74?

Median statistic. When a distribution is symmetric, the mean and median will equal. So, when sampling from a symmetric population, it would seem that we would be indifferent in using either the...

lathu2nd please answer all in step by step manner. please dont give wrong answer. thank you. q1: Formulas: x-bar i m phat 1r m estimate i m phat = x I n p = X I N x-bar i T (s 1 xi?) p-hat i z \\l...

BA 1605: Midterm Recap (Due: Feb. 27, 2015) Name _____________________________ 50 Student ID _____________________________ Section 01B 10:00~11:20 am Section 02B 01:00~02:20 pm [Questions 4 ~ 7] The...

Scanned by CamScanner Sampling and Sampling Distribution (Ch. 5 & 9) BA1605-07 (Sampling) 1 Polls BA1605-07 (Sampling) 2 Statistical Inference Involves Estimation Population? Hypothesis testing...

Student: Brandy Freytag Date: 7/11/16 Instructor: Doug LeVeque, Beverly Wood Assignment: MSL Chapter 7 HW Course: MATH_211_1841_May_2016(LeVeque) 1. Two symbols are used for the mean: and x. a. Which...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

6. The human intelligence quotient, or IO, is computed according to the following formula: 10 =- tar Mental Age -x 100. m sigo Chronological Age mobna A The Mental Age part of the formula is measured...

An analyst summarizes the following information for a firm (dollar amounts in millions); Analyze the growth of average common shareholders' equity in2009. 2009 2008 2007 Common sharehoiders equity...

What is the purpose of an oral presentation? What guidelines should be followed in an oral presentation?

1 h 1 5 min Exit Exam 4 2 out of 5 0 Review Later What effect will each of the following actions ALONE have on return on equity? Select ALL correct answers. Selling assets above net book value will...

Describe different problems that can happen if we apply the OLS method to estimate a linear probability model (LPM).

A sample preparation for a chemical measurement is completed correctly by 25% of the lab technicians, completed with a minor error by 70%, and completed with a major error by 5%. (a) If a technician...

A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly, what is the probability that it is a valid number?

Suppose your vehicle is licensed in a state that issues license plates that consist of three digits (between 0 and 9) followed by three letters (between A and Z). If a license number is selected...

What is the effective annual rate ( EAR ) for a nominal rate ( monthly compounding ) of 5 . 5 2 %

The management of Mitchell Labs decided to go private in 2002 by buying all 3.10 million of its outstanding shares at $20.30 per share. By 2006, management had restructured the company by selling off...

Company A has 6,000 shares. The initial price was $3.50 /share and the current price is 3.75/ share. Company B initially had 900 shares at $10 /share and currently has 1,800 shares at $5.50 /share....