Binomial Distribution If you flip a coin 3 times, what is the probability that you will get exactly 1 tails? There is more than one way to do this problem,

Slides:

Advertisements

Similar presentations

Lesson Objective Be able to calculate probabilities for Binomial situations Begin to recognise the conditions necessary for a Random variable to have a.

Advertisements

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 5.4.

QBM117 Business Statistics Probability Distributions Binomial Distribution 1.

ฟังก์ชั่นการแจกแจงความน่าจะเป็น แบบไม่ต่อเนื่อง Discrete Probability Distributions.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 5-1 Chapter 5 Some Important Discrete Probability Distributions Statistics.

CHAPTER 13: Binomial Distributions

Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 5-1 Statistics for Managers Using Microsoft® Excel 5th Edition.

The Binomial Distribution

Probability Distributions Discrete. Discrete data Discrete data can only take exact values Examples: The number of cars passing a checkpoint in 30 minutes.

Chapter – Binomial Distributions Geometric Distributions

5.1 Sampling Distributions for Counts and Proportions.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 4-1 Introduction to Statistics Chapter 5 Random Variables.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 5-1 Chapter 5 Some Important Discrete Probability Distributions Statistics.

Discrete Probability Distributions

Chapter 5 Discrete Probability Distributions © McGraw-Hill, Bluman, 5 th ed, Chapter 5 1.

Binomial & Geometric Random Variables

Discrete Probability Distributions

Discrete Probability Distributions

Chapter 8 Binomial and Geometric Distributions

Chapter 8 The Binomial and Geometric Distributions

The Binomial Distribution

Statistics Alan D. Smith.

Bluman, Chapter 51. guessing Suppose there is multiple choice quiz on a subject you don’t know anything about…. 15 th Century Russian Literature; Nuclear.

Quiz 4  Probability Distributions. 1. In families of three children what is the mean number of girls (assuming P(girl)=0.500)? a) 1 b) 1.5 c) 2 d) 2.5.

The Binomial Distribution

Binomial & Geometric Random Variables §6-3. Goals: Binomial settings and binomial random variables Binomial probabilities Mean and standard deviation.

McGraw-Hill/IrwinCopyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 4 and 5 Probability and Discrete Random Variables.

1 Overview This chapter will deal with the construction of probability distributions by combining the methods of Chapter 2 with the those of Chapter 4.

Thermo & Stat Mech - Spring 2006 Class 16 More Discussion of the Binomial Distribution: Comments & Examples jl.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 5-1 Chapter 5 Some Important Discrete Probability Distributions Basic Business Statistics.

40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Statistics Lesson: ST-5 The Binomial Distribution The Binomial Distribution Learning Outcome.

Binomial Distributions Calculating the Probability of Success.

The Binomial Distribution. Binomial Experiment.

Business and Finance College Principles of Statistics Eng. Heba Hamad 2008.

Discrete Probability Distributions

Chapter 7 Lesson 7.5 Random Variables and Probability Distributions

Chapter 5 Lecture 2 Sections: 5.3 – 5.4.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 5-1 Chapter 5 Some Important Discrete Probability Distributions Basic Business Statistics.

Bernoulli Trials Two Possible Outcomes –Success, with probability p –Failure, with probability q = 1  p Trials are independent.

Binomial Probability Distribution

 5-1 Introduction  5-2 Probability Distributions  5-3 Mean, Variance, and Expectation  5-4 The Binomial Distribution.

Ch 5 Probability: The Mathematics of Randomness Random Variables and Their Distributions A random variable is a quantity that (prior to observation)

Chapter 5 Discrete Probability Distributions. Introduction Many decisions in real-life situations are made by assigning probabilities to all possible.

4.2 Binomial Distributions

Your 3rd quiz will cover sections a){HHH,HTT,THT,TTH,THH,HTH,HHT,TTT} {0,1,2,3} b) {1/8,3/8,3/8,1/8} d) P(x=2 or x=3)= P(x=2)+P(x=3)=3/8+1/8=1/2.

The Binomial Distributions

Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc. Chap 5-1 Business Statistics: A Decision-Making Approach 7 th Edition Chapter.

Chapter 6: Random Variables

1. Binomial Trials: Success/Failure 2. Probability of k Successes 1.

Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 5-1 Chapter 5 Some Important Discrete Probability Distributions Business Statistics,

Chapter 5 Discrete Probability Distributions. Overview Introduction O 5-1 Probability Distributions O 5-2 Mean, Variance, Standard Deviation, and Expectation.

Section 6.3 Day 1 Binomial Distributions. A Gaggle of Girls Let’s use simulation to find the probability that a couple who has three children has all.

Binomial Distribution. Bernoulli Trials Repeated identical trials are called Bernoulli trials if: 1. There are two possible outcomes for each trial, denoted.

Probability Distributions. Constructing a Probability Distribution Definition: Consists of the values a random variable can assume and the corresponding.

+ Binomial and Geometric Random Variables Textbook Section 6.3.

Chapter 5 Discrete Probability Distributions 1. Chapter 5 Overview 2 Introduction  5-1 Probability Distributions  5-2 Mean, Variance, Standard Deviation,

CHAPTER 5 Discrete Probability Distributions. Chapter 5 Overview  Introduction  5-1 Probability Distributions  5-2 Mean, Variance, Standard Deviation,

Discrete Probability Distributions Chapter 5 1. Chapter 5 Overview 2 Introduction 5-1 Probability Distributions 5-2 Mean, Variance, Standard Deviation,

Binomial Probability Distributions. Binomial Probability Distributions are important because they allow us to deal with circumstances in which the outcomes.

Chapter 7 Lesson 7.5 Random Variables and Probability Distributions

Negative Binomial Experiment

8.1 The Binomial Distributions

Discrete Probability Distributions

Samples and Populations

Statistics 1: Elementary Statistics

More Discussion of the Binomial Distribution: Comments & Examples

The Binomial and Geometric Distributions

More Discussion of the Binomial Distribution: Comments & Examples

Statistics 1: Elementary Statistics

Bernoulli Trials Two Possible Outcomes Trials are independent.

Presentation transcript:

Binomial Distribution If you flip a coin 3 times, what is the probability that you will get exactly 1 tails? There is more than one way to do this problem, but the easiest is by using the methods for a binomial distribution.

Binomial Distribution Binomial distribution applies to cases where there are only two possible outcomes: head or tail, success or failure and defective item or good item. Requirements for using Binomial Distribution -Each outcome is independent of the others -There are only two possible outcomes (success or failure) -The probability of each outcome is always the same -The number of trials must be fixed.

Here are some exercises to look at. Determine if X has a binomial distribution, and why? 1) You observe the sex of the next 20 children born at a local hospital; X is the number of girls among them. 2) A couple decides to continue to have children until their first girl is born; X is the total number of children the couple has. 3) Joe buys a state lottery ticket every week. The count X is the number of times a year that he wins a prize.

1) It may be binomial if we assume that there are no twins or other multiple births among the ext 20, and that for all births, the probability that the baby is female is the same. 2) No – the number of observations is not fixed. 3) Assuming that Joe’s chance of winning the lottery is the same every week and that a year consists of 52 weeks (observations), this would be binomial.

Binomial Distribution Let p = probability that an item is defective q = probability that an item is good The item can either be good or defective. Therefore, q = 1-p If n items are produced, find the probability of exactly r defective items.

Binomial Distribution The formula for finding the probability of “r” things occurring out of “n” trials is… Where p is the probability of a success and q is the probability of a failure and…

Back to the coin problem For our problem p=probability of a tails (.5) and q=probability of a heads (.5) so our equation would be…

Binomial Distribution A sample of eleven electric bulbs is drawn every day from those manufactured at a plant. Probabilities of defective bulbs are random and independent of previous results. The probability that a bulb is defective is What is the probability of finding exactly three defective bulbs in a sample? What is the probability of finding three or more defective bulbs in a sample?

Binomial Distribution No. of defective bulbs Probability 0(1)(0.04) 0 (0.96) 11 = C 1 (0.04) 1 (0.96) 10 = C 2 (0.04) 2 (0.96) 9 = C 3 (0.04) 3 (0.96) 8 =

Binomial Distribution Pr[3 defective bulbs] = Pr[3 or more def.] = 1- Pr[0 def.] – Pr[1 def.] – Pr[2 def.] = 1 – – =

Binomial Distribution Standard Deviation Mean Variance

Binomial Distribution For p = 0.35 and n = 10