Problem%20Set%2001_2010_2011[1]

# Problem%20Set%2001_2010_2011[1] - Middle East Technical...

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

Middle East Technical University 2010-2011 Fall Department of Economics ECON 206 Instructor: Ozan ERUYGUR Research Assistant: Pelin AKÇAGÜN PROBLEM SET 01 EXPECTATION AND VARIANCE OPERATORS PROBLEM 1 (Exercise 4.17 from textbook) Prove Theorem 4.5. Theorem 4.5: Let c be a constant, and let g(Y), g 1 (Y), g 2 (Y), ... , g k (Y) be functions of a continuous random variable Y. Then the following results hold: 1. E(c) = c. 2. E[cg(Y)] = cE[g(Y)]. 3. E[g 1 (Y)+ g 2 (Y)+ . .. +g k (Y)] = E[g 1 (Y)]+ E[g 2 (Y)]+ . .. +E[g k (Y)]. PROBLEM 2 (Exercise 4.18 from textbook) If Y is a continuous random variable with density function f(Y), use Theorem 4.5 to prove that . 22 () ( ) [() ] VY EY σ= = 2 PROBLEM 3 (Exercise 4.20 from textbook) If Y is a continuous random variable with mean μ and variance σ 2 and a and b are constants, use Theorem 4.5 to prove the following: a. E(aY+b)=aE(Y)+b=aμ+b. b. V(aY + b) = a 2 V(Y) = a 2 σ 2 PROBLEM 4 (Exercise 4.24 from textbook) The proportion of time Y that an industrial robot is in operation during a 40-hour week is a random variable with probability density function 2, 0 1 0, yy fy elsewhere ≤≤ = a. Find E(Y) and V(Y).

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 03/22/2012 for the course ECON 106 taught by Professor Kücüksenel during the Spring '12 term at Middle East Technical University.

### Page1 / 3

Problem%20Set%2001_2010_2011[1] - Middle East Technical...

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

View Full Document
Ask a homework question - tutors are online