introduction to probability

... period. We take r to be the interest Chapter 1 Introduction to Probability Theory 1.1 The Binomial Asset Pricing Model The binomial asset pricing model provides a powerful tool to understand arbitrage ... take d and u to satisfy 0 d1u , so change of the stock price from S 0 to dS 0 represents a downward movement, and change of the stock price from S 0 to uS 0 represents an...

Ngày tải lên: 18/10/2013, 03:20

... of the exercises is available to instructors. Historical remarks: Introductory probability is a subject in which the funda- mental ideas are still closely tied to those of the founders of the ... Scholar (Princeton: Princeton University Press, 1953). 34 CHAPTER 1. DISCRETE PROBABILITY DISTRIBUTIONS then he needs two games to win and B needs three games to win; and so, if the touna...

Ngày tải lên: 20/12/2013, 19:15

... more appropriate to assign a distribution function which assigns probability .513 to the outcome boy and probability .487 to the outcome girl than to assign probability 1/2 to each outcome. This ... Snell’s Introduction to Probability The CHANCE Project 1 Version dated 4 July 2006 1 Copyright (C) 2006 Peter G. Doyle. This work is a version of Grinstead and Snell’s Intro...

Ngày tải lên: 21/02/2014, 09:20

... more appropriate to assign a distribution function which assigns probability .513 to the outcome boy and probability .487 to the outcome girl than to assign probability 1/2 to each outcome. This ... applied to human affairs. 9 Exercises 1 Modify the program CoinTosses to toss a coin n times and print out after every 100 tosses the proportion of heads minus 1/2. Do these num...

Ngày tải lên: 15/03/2014, 09:20

... inequality, 60 monotone class theorem, 52 monotone convergence, 45 open set, 11 Poisson distribution, 21 Poisson’s Theorem, 24 probability measure, 12 probability space, 12 product of probability spaces, ... σ(G 0 ) can be shown in the same way.  1.2 Probability measures Now we introduce the measures we are going to use: Definition 1.2.1 [probability measure, probability space] L...

Ngày tải lên: 31/03/2014, 16:23

Ngày tải lên: 31/03/2014, 16:24

... and “his” are used sparingly in this course t o enhance communication, they are not intended to be gender driven or to affront or discriminate against anyone.

Ngày tải lên: 31/03/2014, 16:24

Ngày tải lên: 08/04/2014, 12:21

Ngày tải lên: 08/04/2014, 12:21

... different objects into the 1st box, and then  n−a b  ways of putting b different objects into the 2nd and then one way to put the remaining objects into the 3rd box. Thus the total number of ways ... S n −n/2 tends to infinity as n tends to infinity. While the difference will be small compared to n/2, it will not tend to 0. On the other hand the difference S n /n −1/2 does tend to 0....

Ngày tải lên: 05/06/2014, 11:31