Lecture 03-2007

# Lecture 03-2007 - Probability Theory and Measure: Lecture...

This preview shows pages 1–3. Sign up to view the full content.

1 Probability Theory and Measure: Lecture III I. Uniform Probability Measure: A. I think that Bieren’s discussion of the uniform probability measure provides a firm basis for the concept of probability measure. 1. First, we follow the conceptual discussion of placing ten balls numbered 0 through 9 into a container. Next, we draw out an infinite 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 random numbers such as: Table 1. Random Draws of Single Digits Ball Drawn Draw 1 Draw 2 Draw 3 1 7 0 3 2 4 2 0 3 1 9 2 4 4 6 2 5 8 4 0 6 3 5 4 Taking each column, we can generate three random numbers {0.741483, 0.029645, 0.302204}. Note that each of these sequences are contained in the unit interval   0,1  . The primary point of the demonstration is that the number draw (   0,1 x   ) is a probability measure. a. Taking 0.741483 x as the example, we want to prove that     0, 0.741483 0.741483 Px  . To do this we want 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 first number in Table 1 less than 7, it is 7 ~{0,1,2,3,4,5,6}. Thus, without consider the second number, the probability of drawing a number less than 0.741483 is somewhat greater than 7/10. c. Next, we consider drawing a second number given that the first number drawn is greater than or equal to 7. Now, we are interested

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
AEB 6933 Mathematical Statistics for Food and Resource Economics Lecture III Professor Charles B. Moss
This is the end of the preview. Sign up to access the rest of the document.

## Lecture 03-2007 - Probability Theory and Measure: Lecture...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online