Lecture11-2010 - Binomial and Normal Random Variables Charles B Moss I Bernoulli Random Variables A The Bernoulli distribution characterizes the

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Binomial and Normal Random Variables Charles B. Moss July 14, 2010 I. Bernoulli Random Variables A. The Bernoulli distribution characterizes the coin toss. Specifcally, there are two events X =0 , 1 with X = 1 occurring with probabil- ity p . The probability distribution Function P [ X ] can be written as P [ X ]= p x (1 p ) x (1) B. Next, we need to develop the probability oF where both and are identically distributed. IF the two events are independent, the probability becomes P [ X,Y ]= P [ X ] P [ Y ]= p x p y (1 p ) 1 - x (1 p ) 1 - y = p x + y (1 p ) 2 - x - y (2) C. Now, this density Function is only concerned with three outcomes Z = X + Y = { 0 , 1 , 2 } . 1. There is only one way each For Z =0or Z =2 . a) Specifcally For Z =0, X =0and Y =0 . b) Similarly, For Z =2, X =1and Y =1 . 2. However, For Z = 1 either X =1and Y =0or X =0and
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AEB 6571 Econometric Methods I Professor Charles B. Moss Lecture XI Fall 2010 P [ Z =0 ]= p 0 (1 p ) 2 - 0 P [ Z =1 ]= P [
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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.

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Lecture11-2010 - Binomial and Normal Random Variables Charles B Moss I Bernoulli Random Variables A The Bernoulli distribution characterizes the

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