Lecture08-2010

# Lecture08-2010 - Mean and Higher Moments Charles B Moss July 9 2010 I Expected Value A Denition 4.1.1 Let X be a discrete random variable taking

This preview shows pages 1–4. Sign up to view the full content.

Mean and Higher Moments Charles B. Moss July 9, 2010 I. Expected Value A. Defnition 4.1.1 :Le t X be a discrete random variable taking the value x with probability P ( x i ) ,i =1 , 2 , ··· . Then the expected value (expectation or mean) of X , denoted E [X], is deFned to be E[X]= i=1 x i P(x i ) if the series converges absolutely. 1. We can write E [X] = + x i i )+ x i i ) where in the Frst summation we sum for i such that x i > 0 and in the second summation we sum for i such that x i < 0. 2. If + x i P ( x i )= and x i P ( x i then E [X] does not exist. 3. If + x i P ( x i and x i P ( x i ) is Fnite then we say . 4. If P ( x i −∞ and + x i P ( x i ) is Fnite then we say that −∞ . B. A practical application: 1. Given that each face of the die is equally likely, what is the expected value of the role of the die? 2. What is the expected value of a two-die role? C. Expectation has several applications in risk theory. In general, the expected value is the value we expect to occur. ±or example, if we assume that the crop yield follows a binomial distribution as depicted in ±igure 1, the expected return on the crop given that the price is \$3 and the cost per acre is \$40, becomes \$ 95 per acre as demonstrated in Table 3. 1

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

View Full Document
AEB 6571 Econometric Methods I Professor Charles B. Moss Lecture VIII Fall 2010 Table 1: Expected Value of a Single Die Role Number Probability x i P ( x i ) 1 0.167 0.167 2 0.167 0.333 3 0.167 0.500 4 0.167 0.667 5 0.167 0.833 6 0.167 1.000 Total 3.500 Table 2: Expected Value of a Two-Die Role Die 1 Die 2 Number x i P ( x i ) Die 1 Die 2 Number x i P ( x i ) 1 1 2 0.056 1 4 5 0.139 2 1 3 0.083 2 4 6 0.167 3 1 4 0.111 3 4 7 0.194 4 1 5 0.139 4 4 8 0.222 5 1 6 0.167 5 4 9 0.250 6 1 7 0.194 6 4 10 0.278 1 2 3 0.083 1 5 6 0.167 2 2 4 0.111 2 5 7 0.194 3 2 5 0.139 3 5 8 0.222 4 2 6 0.167 4 5 9 0.250 5 2 7 0.194 5 5 10 0.278 6 2 8 0.222 6 5 11 0.306 1 3 4 0.111 1 6 7 0.194 2 3 5 0.139 2 6 8 0.222 3 3 6 0.167 3 6 9 0.250 4 3 7 0.194 4 6 10 0.278 5 3 8 0.222 5 6 11 0.306 6 3 9 0.250 6 6 12 0.333 Total 7.000 2
AEB 6571 Econometric Methods I Professor Charles B. Moss

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 07/15/2011 for the course AEB 6180 taught by Professor Staff during the Spring '10 term at University of Florida.

### Page1 / 8

Lecture08-2010 - Mean and Higher Moments Charles B Moss July 9 2010 I Expected Value A Denition 4.1.1 Let X be a discrete random variable taking

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online