Suppose that X1,...,X5 is a random sample from the uniform distribution with parameter θ (i.e., these are independent uniform random variables with parameter θ, where θ is unknown). Define the following estimator (a random variable that is a function of X1,...,X5):     Xmax = k max(X1,...,X5), where k will be selected later. (a) Find the density of Xmax (it will depend on θ and k). (b) Find k such that Xmax is an unbiased estimator for θ.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question

Suppose that X1,...,X5 is a random sample from the uniform distribution with parameter θ (i.e., these are independent uniform random variables with parameter θ, where
θ is unknown). Define the following estimator (a random variable that is a function of X1,...,X5):     Xmax = k max(X1,...,X5), where k will be selected later.


(a) Find the density of Xmax (it will depend on θ and k).
(b) Find k such that Xmax is an unbiased estimator for θ.

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON