My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum

LinkBack Thread Tools Display Modes
January 21st, 2018, 09:42 AM   #1
Senior Member
Joined: Jan 2016
From: Blackpool

Posts: 100
Thanks: 2

Probability Estimators question

Suppose the random variables $X_{1}...x_{n}$ are independent and that for i=1,2...n
\[X_{i}~Poisson(w_{i}\lambda)\] for $w_{i}>0$ lambda>0

for some weights $w_{1}...w_{n}$

calculate the bias if the sample mean $X_{n}$ is used as an estimator for lambda. What constraint can be placed on the weights to ensure the estimator is unbiased?
Jaket1 is offline  
January 21st, 2018, 09:55 AM   #2
Senior Member
Joined: Oct 2009

Posts: 712
Thanks: 238

Well, how do we define the bias? What happens if you compute it?
Micrm@ss is offline  
January 21st, 2018, 12:04 PM   #3
Senior Member
romsek's Avatar
Joined: Sep 2015
From: USA

Posts: 2,266
Thanks: 1198

$E\left[\dfrac 1 n \sum \limits_{i=1}^n~X_i \right] = \dfrac 1 n \sum \limits_{i=1}^n~E[X_i] = \dfrac \lambda n \sum \limits_{i=1}^n~w_i$

can you finish it?
romsek is online now  

  My Math Forum > High School Math Forum > Probability and Statistics

estimators, probability, question

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Maximum Likelihood Estimators Actuary Calculus 0 July 13th, 2015 04:39 AM
Unbiased Estimators Artus Advanced Statistics 1 March 7th, 2013 01:35 PM
maximum-likelihood estimators graphist_groupist Advanced Statistics 1 July 16th, 2012 11:28 PM
Log Normal Mean Estimators Zazu Algebra 0 May 21st, 2009 05:03 AM
method of moment estimators zve5 Advanced Statistics 1 September 26th, 2008 05:11 AM

Copyright © 2019 My Math Forum. All rights reserved.