Discrete Distributions. Random Variable - A numerical variable whose value depends on the outcome of a chance experiment.

Slides:

Advertisements

Similar presentations

Discrete Distributions

Advertisements

AP Statistics Chapter 7 – Random Variables. Random Variables Random Variable – A variable whose value is a numerical outcome of a random phenomenon. Discrete.

Rules for Means and Variances

Chapter 7 Discrete Distributions. Random Variable - A numerical variable whose value depends on the outcome of a chance experiment.

Business Statistics for Managerial Decision

Section 7A: Fundamentals of Probability Section Objectives Define outcomes and event Construct a probability distribution Define subjective and empirical.

Chapter 5.1 & 5.2: Random Variables and Probability Mass Functions

Random Variables Probability Continued Chapter 7.

Sections 4.1 and 4.2 Overview Random Variables. PROBABILITY DISTRIBUTIONS This chapter will deal with the construction of probability distributions by.

Linear Transformation and Statistical Estimation and the Law of Large Numbers Target Goal: I can describe the effects of transforming a random variable.

1. Variance of Probability Distribution 2. Spread 3. Standard Deviation 4. Unbiased Estimate 5. Sample Variance and Standard Deviation 6. Alternative Definitions.

5.1 Sampling Distributions for Counts and Proportions.

Random Variables A Random Variable assigns a numerical value to all possible outcomes of a random experiment We do not consider the actual events but we.

Business 90: Business Statistics

CHAPTER 6 Random Variables

 The Law of Large Numbers – Read the preface to Chapter 7 on page 388 and be prepared to summarize the Law of Large Numbers.

Chapter 16: Random Variables

Unit 4 Starters. Starter Suppose a fair coin is tossed 4 times. Find the probability that heads comes up exactly two times.

Stat 1510: Introducing Probability. Agenda 2  The Idea of Probability  Probability Models  Probability Rules  Finite and Discrete Probability Models.

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

AP Statistics: Section 8.2 Geometric Probability.

1. Population Versus Sample 2. Statistic Versus Parameter 3. Mean (Average) of a Sample 4. Mean (Average) of a Population 5. Expected Value 6. Expected.

Statistical Experiment A statistical experiment or observation is any process by which an measurements are obtained.

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 11 Section 1 – Slide 1 of 34 Chapter 11 Section 1 Random Variables.

Probability Distributions Random Variables * Discrete Probability Distributions * Mean, Variance, and Standard Deviation * Expected Value.

Applied Business Forecasting and Regression Analysis Review lecture 2 Randomness and Probability.

Expected values and variances. Formula For a discrete random variable X and pmf p(X): Expected value: Variance: Alternate formula for variance:  Var(x)=E(X^2)-[E(X)]^2.

Probability Distributions. Essential Question: What is a probability distribution and how is it displayed?

Section 5.1 Expected Value HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights.

5.3 Random Variables  Random Variable  Discrete Random Variables  Continuous Random Variables  Normal Distributions as Probability Distributions 1.

Chapter 5.1 Probability Distributions.  A variable is defined as a characteristic or attribute that can assume different values.  Recall that a variable.

Chapter 5: Random Variables and Discrete Probability Distributions

P. STATISTICS LESSON 8.2 ( DAY 1 )

DISCRETE PROBABILITY DISTRIBUTIONS

Discrete probability distributions 3)For every possible x value, 0 < P(x) < 1. 4) For all values of x, S P(x) = 1.

Binomial Experiment A binomial experiment (also known as a Bernoulli trial) is a statistical experiment that has the following properties:

Chapter 16: Random Variables

Probability Distributions

LINEAR FUNCTION OF A RANDOM VARIABLE If x is a random variable and a and b are numerical constants, then the random variable y is defined by and.

Lesson Objective Understand what we mean by a Random Variable in maths Understand what is meant by the expectation and variance of a random variable Be.

Sections 5.1 and 5.2 Review and Preview and Random Variables.

The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 6 Random Variables 6.1 Discrete and Continuous.

Random Variables Ch. 6. Flip a fair coin 4 times. List all the possible outcomes. Let X be the number of heads. A probability model describes the possible.

Probability Distributions

Probability Distributions, Discrete Random Variables

AP Statistics Monday, 30 November 2015 OBJECTIVE TSW begin the study of discrete distributions. EVERYONE needs a calculator. The tests are graded.

AP STATISTICS Section 7.1 Random Variables. Objective: To be able to recognize discrete and continuous random variables and calculate probabilities using.

Chapter 7 Random Variables and Discrete Distributions.

6.1 Discrete and Continuous Random Variables Objectives SWBAT: COMPUTE probabilities using the probability distribution of a discrete random variable.

Chapter 7.2. The __________ of a discrete random variable, X, is its _________ _____________. Each value of X is weighted by its probability. To find.

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.

Chapter 8: The Binomial and Geometric Distributions 8.2 – The Geometric Distributions.

Chapter Discrete Probability Distributions 1 of 26 4  2012 Pearson Education, Inc. All rights reserved.

Discrete Distributions

Random Variables and Probability Distribution (2)

Chapter 4 Discrete Probability Distributions.

Chapter 4 Discrete Probability Distributions.

Discrete Distributions

Discrete Probability Distributions

CHAPTER 6 Random Variables

Expected Value.

Probability Key Questions

Discrete Distributions

Discrete Distributions

Modeling Discrete Variables

Discrete Distributions.

Discrete Distributions

MATH 2311 Section 3.1.

Presentation transcript:

Discrete Distributions

Random Variable - A numerical variable whose value depends on the outcome of a chance experiment

Two types: Discrete – count of some random variable Continuous – measure of some random variable

Discrete Probability Distribution Gives the values associated with each possible x value Usually displayed in a table, but can be displayed with a histogram or formula

Properties for a discrete probability distribution 1)For every possible x value, 0 < P(x) < 1. 2) For all values of x, ΣP(x) = 1.

Suppose you toss 3 coins & record the number of heads. The random variable X defined as... Create a probability distribution. Create a probability histogram. The number of heads tossed X0123X0123 P(X)

Let x be the number of courses for which a randomly selected student at a certain university is registered. X P(X) ? P(x = 4) = P(x < 4) = What is the probability that the student is registered for at least five courses? Why does this not start at zero? P(x > 5) =.61

Formulas for mean & variance Found on formula card!

Let x be the number of courses for which a randomly selected student at a certain university is registered. X P(X) What is the mean and standard deviations of this distribution?  4.66 & σ =

Here ’ s a game: If a player rolls two dice and gets a sum of 2 or 12, he wins $20. If he gets a 7, he wins $5. The cost to roll the dice one time is $3. Is this game fair? A fair game is one where the cost to play EQUALS the expected value! X0520 P(X)7/91/61/18 NO, since  = $1.944 which is less than it cost to play ($3).

Linear function of a random variable If x is a random variable and a and b are numerical constants, then the random variable y is defined by and The mean is changed by addition & multiplication! ONLY The standard deviation is ONLY changed by multiplication!

Let x be the number of gallons required to fill a propane tank. Suppose that the mean and standard deviation are 318 gal. and 42 gal., respectively. The company is considering the pricing model of a service charge of $50 plus $1.80 per gallon. Let y be the random variable of the amount billed. What is the mean and standard deviation for the amount billed? μ = $ & σ = $75.60

Linear combinations Just add or subtract the means! add If independent, always add the variances!

A nationwide standardized exam consists of a multiple choice section and a free response section. For each section, the mean and standard deviation are reported to be meanSD MC386 FR307 If the test score is computed by adding the multiple choice and free response, then what is the mean and standard deviation of the test?  68 & σ =