Section 15.8 The Binomial Distribution. A binomial distribution is a discrete distribution defined by two parameters: The number of trials, n The probability.

Slides:

Advertisements

Similar presentations

Probability Distribution

Advertisements

Special random variables Chapter 5 Some discrete or continuous probability distributions.

Discrete Uniform Distribution

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

The Bernoulli distribution Discrete distributions.

Probability Distribution

5.1 Sampling Distributions for Counts and Proportions.

Bernoulli Distribution

A random variable that has the following pmf is said to be a binomial random variable with parameters n, p The Binomial random variable.

McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Discrete Random Variables Chapter 4.

Binomial Distributions Introduction. There are 4 properties for a Binomial Distribution 1. Fixed number of trials (n) Throwing a dart till you get a bulls.

4.5 Comparing Discrete Probability Distributions.

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}.

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

Binomial Probability Distribution

Probability Distributions BINOMIAL DISTRIBUTION. Binomial Trials There are a specified number of repeated, independent trials There are a specified number.

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

Binomial Distributions. Quality Control engineers use the concepts of binomial testing extensively in their examinations. An item, when tested, has only.

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

King Saud University Women Students

Section 5.2 Binomial Distribution HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All.

Math b (Discrete) Random Variables, Binomial Distribution.

Methodology Solving problems with known distributions 1.

The Binomial Distribution

LECTURE 12 TUESDAY, 10 MARCH STA 291 Spring

4.2 Binomial Distributions

Ch. 15H continued. * -applied to experiments with replacement ONLY(therefore…..independent events only) * -Note: For DEPENDENT events we use the “hypergeometric.

1 Week NORMAL DISTRIBUTION BERNOULLI TRIALS BINOMIAL DISTRIBUTION EXPONENTIAL DISTRIBUTION UNIFORM DISTRIBUTION POISSON DISTRIBUTION.

6.2 BINOMIAL PROBABILITIES.  Features  Fixed number of trials (n)  Trials are independent and repeated under identical conditions  Each trial has.

This is a discrete distribution. Situations that can be modeled with the binomial distribution must have these 4 properties: Only two possible outcomes.

DISCRETE PROBABILITY MODELS

LECTURE 18 TUESDAY, 27 OCTOBER STA 291 Fall

Section 9-3 Probability. Probability of an Event if E is an event in a sample space, S, of equally likely outcomes, then the probability of the event.

1 7.3 RANDOM VARIABLES When the variables in question are quantitative, they are known as random variables. A random variable, X, is a quantitative variable.

Chapter 7 Section 5.  Binomial Distribution required just two outcomes (success or failure).  Multinomial Distribution can be used when there are more.

Chapter 5 Joint Probability Distributions and Random Samples  Jointly Distributed Random Variables.2 - Expected Values, Covariance, and Correlation.3.

Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Chapter 5 Discrete Random Variables.

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.

Chap 5-1 Chapter 5 Discrete Random Variables and Probability Distributions Statistics for Business and Economics 6 th Edition.

C: Expectation D: The Binomial Distribution 23CD.

2.2 Discrete Random Variables 2.2 Discrete random variables Definition 2.2 –P27 Definition 2.3 –P27.

Binomial Distribution

Covariance/ Correlation

Chapter 3 Discrete Random Variables and Probability Distributions

Math 4030 – 4a More Discrete Distributions

Supplemental Lecture Notes

Discrete Probability Distributions

Chapter 5 Joint Probability Distributions and Random Samples

Hypergeometric Distribution

Discrete random variable X Examples: shoe size, dosage (mg), # cells,…

3.4 The Binomial Distribution

ASV Chapters 1 - Sample Spaces and Probabilities

Discrete random variable X Examples: shoe size, dosage (mg), # cells,…

MATH 2311 Section 3.2.

Chapter 5: Some Discrete Probability Distributions:

Chapter 3 Discrete Random Variables and Probability Distributions

Some Discrete Probability Distributions

Binomial Distribution

Some Discrete Probability Distributions

Known Probability Distributions

MATH 2311 Section 3.2.

Some Discrete Probability Distributions

Bernoulli Trials Two Possible Outcomes Trials are independent.

Known Probability Distributions

Known Probability Distributions

Known Probability Distributions

Each Distribution for Random Variables Has:

Known Probability Distributions

Chapter 11 Probability.

Binomial Distribution

Presentation transcript:

Section 15.8 The Binomial Distribution

A binomial distribution is a discrete distribution defined by two parameters: The number of trials, n The probability of success, p The discrete random variable (X) is applied to sampling with replacement. The probability distribution associated with this variable is the binomial probability distribution. (For sampling without replacement, the hypergeometric probability distribution is the model used but is not a part of this course!) X~B ( n, p) is written to indicate that the discrete random variable X is binomially distributed. “ ~ “ reads “is distributed as”

Properties of a Binomial Experiment There is a fixed number of trials: n trials On each one of the n trials, there is only one of two possible outcomes, labeled “success” or “failure” (Bernoulli Trials) Each trial is identical and independent On each of the trials, the probability of a success, p, is always the same, and the probability of a failure, q = 1 – p, is also always the same.

The binomial probability distribution function

For example, the probability function for X~B(6, o.4) means that there are 6 trials and the probability of success is 0.4.

If X~B(5, 0.6), find P(X=4)

Example Suppose a spinner has 3 blue edges and 1 white edge. For each spin we will get either a blue or a white edge. If we call a blue result a “success” and a white result a “failure”, then we have a binomial experiment. Let the random variable X be the number of “successes” or blue results. P(success)= P(failure)= Consider twirling the spinner 3 times, n = 3. Therefore, X = 0, 1, 2, or 3.