2notesmidtermf11

2notesmidtermf11 - Notes for Use During the Midterm Exam;...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Notes for Use During the Midterm Exam; Stat 371; Fall 2011 Not on exam: Finite populations; formula for computing Poisson probabilities by hand; LLN. Probability. Achancemechan ism(CM ) ,whenope ra ted ,p roducesanou tcome .T h es am p l e space is the collection of all possible outcomes of the CM. An event is any collection of outcomes. Before the CM is operated, the probability of the event A ,denotedby P ( A ) ,isanumberthat measures the likelihood that A will occur. If we assume the ELC, then each possible outcome is equally likely to occur. If we assume the ELC, then we assign probabilities to events asfollows .Foranyevent A , P ( A )= The number of outcomes in A The number of outcomes in S . If we do not assume the ELC, there are two possibilities. 1. Suppose that the sample space is ±nite and consists of k possible outcomes: 1 , 2 ,...k .The probability of outcome j is denoted by p j .Each p j 0 and they sum to one. 2. Suppose that the sample space is an in±nite sequence and consists of possible outcomes: 0 , 1 , 2 ,... .Theprobab i l i tyofou tcome j is denoted by p j .Each p j 0 and they sum to one. If A and B are events, then (A or B) is the event that contains allelementsthatareinAand/or B; (AB) is the event that contains all elements that are in bothAandB. Two events, A and B, are called disjoint or mutually exclusivei ftheyhavenoe lemen tsin common; in other words, if AB is the empty set. The Rules of Probability. 1. The probability of the sample space equals 1. 2. For any event A , 0 P ( A ) 1 . 3. If A and B are disjoint events, then P ( A or B )= P ( A )+ P ( B ) . 4. P ( A c )=1 - P ( A ) . 5. If A is a subset of B ,then P ( A ) P ( B ) . 6. For any events A and B , P ( A or B )= P ( A )+ P
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/10/2011 for the course STATS 371 taught by Professor Hanlon during the Fall '11 term at Wisconsin.

Page1 / 2

2notesmidtermf11 - Notes for Use During the Midterm Exam;...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online