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Unformatted text preview: Introduction to Econometrics Econ 322; Summer 2011 Ruby HENRY rhenry@econ.rutgers.edu June 6, 2011 Ruby HENRY () Introduction to Econometrics June 6, 2011 1 / 33 Moments of a Random Variable A random variable X (assume from now on that X is a discrete RV) has a probability distribution function F(x) where < 2 > Prob ( X = x ) = F ( x ) Ruby HENRY () Introduction to Econometrics June 6, 2011 2 / 33 Moments of a Random Variable A random variable X (assume from now on that X is a discrete RV) has a probability distribution function F(x) where < 2 > Prob ( X = x ) = F ( x ) Ruby HENRY () Introduction to Econometrics June 6, 2011 2 / 33 Moments of a Random Variable A random variable X (assume from now on that X is a discrete RV) has a probability distribution function F(x) where < 2 > Prob ( X = x ) = F ( x ) Let Z be the set of all possible values of X . Then the probability distribution function, F, is de&ned < 4 > for all x 2 Z , F ( x ) & < 5 > x 2 Z F ( x ) = 1 Ruby HENRY () Introduction to Econometrics June 6, 2011 2 / 33 Example the expected value of the value showing when you toss a die is Ruby HENRY () Introduction to Econometrics June 6, 2011 3 / 33 Example the expected value of the value showing when you toss a die is E ( X ) = 1 & 1 / 6 + 2 & 1 / 6 + 3 & 1 / 6 + 4 & 1 / 6 + 5 & 1 / 6 + 6 & 1 / 6 = 3 . 5 Ruby HENRY () Introduction to Econometrics June 6, 2011 3 / 33 Example the expected value of the value showing when you toss a die is E ( X ) = 1 & 1 / 6 + 2 & 1 / 6 + 3 & 1 / 6 + 4 & 1 / 6 + 5 & 1 / 6 + 6 & 1 / 6 = 3 . 5 the variance is var ( X ) = E (( X E ( X )) 2 ) = ( 1 3 . 5 ) 2 & 1 / 6 + . . . + ( 6 3 . 5 ) 2 & 1 / 6 = 2 . 91 Ruby HENRY () Introduction to Econometrics June 6, 2011 3 / 33 Properties of Mean and Variance F Suppose we have a new random variable that is a linear function of the random variable X Ruby HENRY () Introduction to Econometrics June 6, 2011 4 / 33 Properties of Mean and Variance F Suppose we have a new random variable that is a linear function of the random variable X e.g. Y = a + bX Ruby HENRY () Introduction to Econometrics June 6, 2011 4 / 33 Properties of Mean and Variance F Suppose we have a new random variable that is a linear function of the random variable X e.g. Y = a + bX what are the moments of Y? Ruby HENRY () Introduction to Econometrics June 6, 2011 4 / 33 Properties of Mean and Variance F Suppose we have a new random variable that is a linear function of the random variable X e.g. Y = a + bX what are the moments of Y? (long way) we can compute the probability density function of Y Ruby HENRY () Introduction to Econometrics June 6, 2011 4 / 33 Properties of Mean and Variance F Suppose we have a new random variable that is a linear function of the random variable X e.g. Y = a + bX what are the moments of Y?...
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This note was uploaded on 09/29/2011 for the course ECON 322 taught by Professor Francisco during the Summer '07 term at Rutgers.
 Summer '07
 Francisco
 Econometrics

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