Lecture 03a

Lecture 03a - PAM 3300 January 27th, 2009 Born today:...

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1 PAM 3300 – January 27 th , 2009 • Born today: – Mozart – Lewis Carroll – Mikhail Baryshnikov – John Roberts – Keith Olbermann • Today is National Chocolate Cake Day PAM 3300 - Announcements • Got Stata? • Office Hours (MVR 107) – Matt: T, Th 10-11:45AM – Maggie: M 12-2PM ; F 10-12 noon – Email: Matt (mjs289) & Maggie (mrj62) • For Thursday: – Holland (1986) – Fryer & Levitt (2004) – Bertrand & Mullainathan (2004) – DiNardo (2007)
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2 PAM 3300 – Statistics Review References • Your PAM 210(0) textbook • These notes will be posted to Blackboard website • Appendices B and C of Wooldridge’s Introductory Econometrics offer a nice review • Problem Set 1 will give you practice at these concepts and techniques
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3 Random Variables • Definition: a random variable (r.v) is one that takes on numerical values, and whose outcome is determined by an experiment or event •E x am p l e s : – Your score on the mid-term – Your starting salary when you leave Cornell – Number of heads I get when I flip a coin 10 times • Context of the experiment can help you know what possible values the random variable can take on Random Variables (con’t) Q: When does the randomness resolve itself? A: After the experiment has been conducted (the value that the r.v takes on is revealed) • Back to the examples: – Once you take the midterm, you will know your score – When you get your first job, you will know your starting salary – Once I flip a coin ten times, I’ll know how many times I got ‘heads’
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4 Random Variables (con’t) • Two types of random variables • Discrete random variable: takes on only a finite number of values –E x am p l e s : • The number that comes up from rolling dice • The number of PAM 3300 students that show up for Thursday’s class • Continuous random variable : takes on any real value with zero probability. – Another (easier) way to think about it: the r.v. can take on a lot of different values •E x p l e s : – Hourly wages in the United States – SAT scores of high school students Characterizing Random Variables • Probability density function (pdf): summarizes the information concerning the possible outcomes of a random variable, and their corresponding probabilities. – In other words, the pdf tells us how likely it is for a random variable to take on particular values
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5 Characterizing Random Variables (con’t) • Discrete random variable – Example: Define r.v. X as the number of heads that come up from flipping a coin twice. ¼ for x = 0 Pdf of X defined as: f(x) = ½ for x = 1 ¼ for x = 2 0 1 1 2 Value of X 1/4 1/4 1/4 1/4 Probability TT TH HT HH Possible Outcomes Characterizing Random Variables (con’t) PDF of Discrete Random Variable: Example 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 012 X Probability = f(x)
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6 Characterizing Random Variables (con’t) • Continuous Random Variables
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This note was uploaded on 03/28/2009 for the course PAM 3300 taught by Professor Matsudaira during the Spring '08 term at Cornell.

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Lecture 03a - PAM 3300 January 27th, 2009 Born today:...

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