Lecture03-2010

# Lecture03-2010 - Probability Theory and Measure: Lecture...

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Probability Theory and Measure: Lecture III Charles B. Moss May 7, 2010 I. Uniform Probability Measure: A. I think that Bierens discussion of the uniform probability measure provides a Frm basis for the concept of probability measure. 1. ±irst, we follow the conceptual discussion of placing ten balls numbered 0 through 9 into a container. Next, we draw out an inFnite sequence of balls out of the container, replacing the ball each time. 2. In Excel, we can mimic this sequence using the function ﬂoor(rand()*10,1). This process will give a sequence of ran- dom numbers such as: Table 1. Random Draws of Single Digits Ball Drawn Draw 1 Draw 2 Draw 3 17 0 3 24 2 0 31 9 2 44 6 2 58 4 0 63 5 4 Taking each column, we can generate three random numbers 0.741483, 0.029645, 0.302204. Note that each of these se- quences are contained in the unit interval Ω = [0 , 1]. The primary point of the demonstration is that the number draw { x Ω=[0 , 1] } is a probability measure. a. Taking x =0 . 741483 as the example, we want to prove that P ([0 ,x . 741483]) = 0 . 741483. To do this we want 1

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AEB 6571 Econometric Methods I Professor Charles B. Moss Lecture III Fall 2010 to work out the probability of drawing a number less than 0.741483. b. As a starting point, what is the probability of drawing the ±rst number in Table 1 less than 7, it is 7 ∼{ 0 , 1 , 2 , 3 , 4 , 5 , 6 } .
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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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Lecture03-2010 - Probability Theory and Measure: Lecture...

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