8 - Lecture 3 Part B

8 - Lecture 3 Part B - Introduction to Econometrics Econ...

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Unformatted text preview: Introduction to Econometrics Econ 322; Summer 2011 Ruby HENRY rhenry@econ.rutgers.edu June 8, 2011 Ruby HENRY () Introduction to Econometrics June 8, 2011 1 / 1 The 2 distribution The Normal distribution is an important distribution for many reasons. However, the Normal distribution is practical only for random variables that can take both positive and negative values. There are many occasions in this course that we will deal with random variables that can only take positive values. The following two probability distributions are de&ned only for positive values: Ruby HENRY () Introduction to Econometrics June 8, 2011 2 / 1 The 2 distribution The Normal distribution is an important distribution for many reasons. However, the Normal distribution is practical only for random variables that can take both positive and negative values. There are many occasions in this course that we will deal with random variables that can only take positive values. The following two probability distributions are de&ned only for positive values: The random variable Y has a Chi-Squared distribution with m degrees of freedom ( Y & 2 ( m ) ) if Y is the sum of m standard normal random variables squared. That is Y & 2 ( m ) if Y = X 2 1 + . . . + X 2 m where X 1 , . . . , X m are all N(0,1). Ruby HENRY () Introduction to Econometrics June 8, 2011 2 / 1 The F distribution A closely related distribution is the &Fdistribution. Ruby HENRY () Introduction to Econometrics June 8, 2011 3 / 1 The F distribution A closely related distribution is the &Fdistribution. In this course we dene the F m , which is dened as Y & F m , if Y = X m where X & 2 ( m ) . Ruby HENRY () Introduction to Econometrics June 8, 2011 3 / 1 The F distribution A closely related distribution is the &Fdistribution. In this course we dene the F m , which is dened as Y & F m , if Y = X m where X & 2 ( m ) . That is, an F random variable is a Chi-squared random variable divided by its degrees of freedom. Ruby HENRY () Introduction to Econometrics June 8, 2011 3 / 1 The Student-t Distribution Another distribution we will come across is the The Student-t Distribution Ruby HENRY () Introduction to Econometrics June 8, 2011 4 / 1 The Student-t Distribution Another distribution we will come across is the The Student-t Distribution Let Z & N ( , 1 ) and let Y & 2 m be two independent random variables. The t = Z p Y / m & t m . Ruby HENRY () Introduction to Econometrics June 8, 2011 4 / 1 The Student-t Distribution Another distribution we will come across is the The Student-t Distribution Let Z & N ( , 1 ) and let Y & 2 m be two independent random variables. The t = Z p Y / m & t m ....
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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.

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8 - Lecture 3 Part B - Introduction to Econometrics Econ...

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