Homework 2 Solutions

Homework 2 Solutions - Homework 2 solution X1 +X3 = + = ,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework 2 – solution 1. a) E X 1 + X 3 2 · = μ + μ 2 = μ , so it’s unbiased. b) E X 1 + X 3 + X n 3 · = μ + μ + μ 3 = μ , so it’s unbiased. c) E X 1 + X 3 +3 X 2 - X 4 5 · = μ + μ +3 μ - μ 5 = 4 μ 5 , so it’s biased with bias equal to 4 μ 5 - μ = - 1 5 μ . d) E (3 X 1 - 2 X 3 ) = 3 μ - 2 μ = μ , so it’s unbiased. e) E X 1 - X 2 + X n/ 2 - X n - 1 + X n · = μ - μ + μ - μ + μ = μ , so it’s unbiased. 2. a) V X 1 + X 3 2 · = σ 2 + σ 2 4 = σ 2 2 . Since it’s unbiased, MSE X 1 + X 3 2 · = V X 1 + X 3 2 · = σ 2 2 . b) V X 1 + X 3 + X n 3 · = σ 2 + σ 2 + σ 2 9 = σ 2 3 . Since it’s unbiased, MSE X 1 + X 3 + X n 3 · = V X 1 + X 3 + X n 3 · = σ 2 + σ 2 + σ 2 9 = σ 2 3 . c) V X 1 + X 3 +3 X 2 - X 4 5 · = σ 2 + σ 2 +9 σ 2 + σ 2 25 = 12 σ 2 25 . So the mean square error is MSE ( X 1 + X 3 +3 X 2 - X 4 5 ) = 12 σ 2 25 + μ 2 25 = 13 σ 2 25 . d)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/18/2011 for the course ECE 083 taught by Professor Best during the Spring '08 term at Lehigh University .

Page1 / 2

Homework 2 Solutions - Homework 2 solution X1 +X3 = + = ,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online