Statistics 1: Elementary Statistics

Slides:

Advertisements

Similar presentations

AP Statistics Section 6.2C Independent Events & The Multiplication Rule.

Advertisements

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

Chapter 12 Probability © 2008 Pearson Addison-Wesley. All rights reserved.

BINOMIAL AND NORMAL DISTRIBUTIONS BINOMIAL DISTRIBUTION “Bernoulli trials” – experiments satisfying 3 conditions: 1. Experiment has only 2 possible outcomes:

Problems Problems 4.17, 4.36, 4.40, (TRY: 4.43). 4. Random Variables A random variable is a way of recording a quantitative variable of a random experiment.

The Binomial Distribution

Unit 5 Section : The Binomial Distribution  Situations that can be reduces to two outcomes are known as binomial experiments.  Binomial experiments.

Discrete Probability Distributions

The Binomial Distribution. Introduction # correct TallyFrequencyP(experiment)P(theory) Mix the cards, select one & guess the type. Repeat 3 times.

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.

The Binomial Distribution

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

Statistics 1: Elementary Statistics Section 5-4. Review of the Requirements for a Binomial Distribution Fixed number of trials All trials are independent.

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics.

Binomial Distributions Calculating the Probability of Success.

Unit 5 Section 5-4 – Day : The Binomial Distribution  The mean, variance, and standard deviation of a variable that has the binomial distribution.

Chapter 7 Lesson 7.5 Random Variables and Probability Distributions

Chapter 5 Lecture 2 Sections: 5.3 – 5.4.

Random Variables. A random variable X is a real valued function defined on the sample space, X : S  R. The set { s  S : X ( s )  [ a, b ] is an event}.

P. STATISTICS LESSON 8.2 ( DAY 1 )

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 Binomial Experiments Section 4-3 & Section 4-4 M A R I O F. T R I O L A Copyright.

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

Binomial Probability Distribution

COMP 170 L2 L17: Random Variables and Expectation Page 1.

Introductory Statistics Lesson 4.2 A Objective: SSBAT determine if a probability experiment is a binomial experiment. SSBAT how to find binomial probabilities.

 Probability: the chance that a particular event will occur.  When do people use probability ◦ Investing in stocks ◦ Gambling ◦ Weather.

Binomial Distribution

Discrete Probability Distributions Chapter 4. § 4.2 Binomial Distributions.

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,

Bernoulli Trials, Geometric and Binomial Probability models.

16-3 The Binomial Probability Theorem. Let’s roll a die 3 times Look at the probability of getting a 6 or NOT getting a 6. Let’s make a tree diagram.

DG minutes 11 th graders psat info --- see board.

Section 5.3 Independence and the Multiplication Rule.

Experiments, Outcomes and Events. Experiment Describes a process that generates a set of data – Tossing of a Coin – Launching of a Missile and observing.

MATH 2311 Section 3.2. Bernoulli Trials A Bernoulli Trial is a random experiment with the following features: 1.The outcome can be classified as either.

The Binomial Probability Distribution

AP Statistics Chapter 8 Section 2. If you want to know the number of successes in a fixed number of trials, then we have a binomial setting. If you want.

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

Discrete Probability Distributions

Probability Distributions

Chapter 7 Lesson 7.5 Random Variables and Probability Distributions

Negative Binomial Experiment

Unit 6 Random Variables.

Section 6.2 Binomial Probability Distribution

Discrete Probability Distributions

Discrete Probability Distributions

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

Section Binomial Distributions

Discrete Probability Distributions

The probability of event P happening is 0. 34

Statistics 1: Elementary Statistics

The Binomial and Geometric Distributions

MATH 2311 Section 3.2.

The Binomial Distribution

Section 8.2: The Geometric Distribution

Random Variables Binomial Distributions

Day 13 AGENDA: DG minutes.

MATH 2311 Section 3.2.

Day 12 AGENDA: DG minutes Work time --- use this time to work on practice problems from previous lessons.

Elementary Statistics

Conditional Probability and the Multiplication Rule

Bernoulli Trials Two Possible Outcomes Trials are independent.

Binomial Distributions

Probability and Counting

CSE 321 Discrete Structures

Probability of Dependent and Independent Events

The Geometric Distribution

MATH 2311 Section 3.2.

Chapter 11 Probability.

Binomial Distribution

Presentation transcript:

Statistics 1: Elementary Statistics Section 5-3

Requirements for a Binomial Distribution Fixed number of trials All trials are independent Each trial: two possible outcomes Probabilities same for each trial

Requirements for a Binomial Distribution Experiment: Flip a coin until you get a “heads” Let x = the number of flips before a heads occurs Not binomial. Why?

Requirements for a Binomial Distribution Experiment: Select 13 cards from a deck of 52 Let x = the number of hearts Not binomial. Why?

Requirements for a Binomial Distribution Experiment: Select a car at random from each of the 50 states Let x = the number of FORDs in the sample Not binomial. Why?

Requirements for a Binomial Distribution Experiment: Select 20 random times during the day and check the traffic light near your house Record the number of times it is red, yellow, or green Not binomial. Why?

Are these Binomial? The number of sixes in 10 rolls of a die The number of contaminated fast-food hamburgers in a random sample of 100 The number of girls in 30 births

Notation for Binomial Distribution S means “success” F means “failure” P(S) = p P(F) = 1 - p = q

More Notation for Binomial Distribution n = the number of trials x = the number of “successes” in n trials P(x) = the probability of exactly x successes in n trials

How do we get P(x)? Binomial Formula