ASSIGNMENT 14 section 10 in the probability and statistics module

Examples: Random Variables. Discrete and Continuous Random Variables. Probability Distributions

Random Variables Examples: Random variable a variable (typically represented by x) that takes a numerical value by chance. Number of boys in a randomly selected family with three children. Possible values:

The Binomial Probability Distribution

The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2017 Objectives After this lesson we will be able to: determine whether a probability

chapter 13: Binomial Distribution Exercises (binomial)13.6, 13.12, 13.22, 13.43

chapter 13: Binomial Distribution ch13-links binom-tossing-4-coins binom-coin-example ch13 image Exercises (binomial)13.6, 13.12, 13.22, 13.43 CHAPTER 13: Binomial Distributions The Basic Practice of Statistics

Chapter 7 presents the beginning of inferential statistics. The two major activities of inferential statistics are

Chapter 7 presents the beginning of inferential statistics. Concept: Inferential Statistics The two major activities of inferential statistics are 1 to use sample data to estimate values of population

Statistical Methods in Practice STAT/MATH 3379

Statistical Methods in Practice STAT/MATH 3379 Dr. A. B. W. Manage Associate Professor of Mathematics & Statistics Department of Mathematics & Statistics Sam Houston State University Overview 6.1 Discrete

Math 160 Professor Busken Chapter 5 Worksheets

Math 160 Professor Busken Chapter 5 Worksheets Name: 1. Find the expected value. Suppose you play a Pick 4 Lotto where you pay 50 to select a sequence of four digits, such as 2118. If you select the same

Math 14 Lecture Notes Ch. 4.3

4.3 The Binomial Distribution Example 1: The former Sacramento King's DeMarcus Cousins makes 77% of his free throws. If he shoots 3 times, what is the probability that he will make exactly 0, 1, 2, or

Mean of a Discrete Random variable. Suppose that X is a discrete random variable whose distribution is : :

Dr. Kim s Note (December 17 th ) The values taken on by the random variable X are random, but the values follow the pattern given in the random variable table. What is a typical value of a random variable

Multinomial Coefficient : A Generalization of the Binomial Coefficient

Multinomial Coefficient : A Generalization of the Binomial Coefficient Example: A team plays 16 games in a season. At the end of the season, the team has 8 wins, 3 ties and 5 losses. How many different

Example 1: Identify the following random variables as discrete or continuous: a) Weight of a package. b) Number of students in a first-grade classroom

Section 5-1 Probability Distributions I. Random Variables A variable x is a if the value that it assumes, corresponding to the of an experiment, is a or event. A random variable is if it potentially can

Binomial Distributions

Binomial Distributions Binomial Experiment The experiment is repeated for a fixed number of trials, where each trial is independent of the other trials There are only two possible outcomes of interest

Chapter 5 Probability Distributions. Section 5-2 Random Variables. Random Variable Probability Distribution. Discrete and Continuous Random Variables

Chapter 5 Probability Distributions Section 5-2 Random Variables 5-2 Random Variables 5-3 Binomial Probability Distributions 5-4 Mean, Variance and Standard Deviation for the Binomial Distribution Random

AP Statistics Ch 8 The Binomial and Geometric Distributions

Ch 8.1 The Binomial Distributions The Binomial Setting A situation where these four conditions are satisfied is called a binomial setting. 1. Each observation falls into one of just two categories, which

Binomial Probability

Binomial Probability Features of a Binomial Experiment 1. There are a fixed number of trials. We denote this number by the letter n. Features of a Binomial Experiment 2. The n trials are independent and

12 Math Chapter Review April 16 th, Multiple Choice Identify the choice that best completes the statement or answers the question.

Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which situation does not describe a discrete random variable? A The number of cell phones per household.

Binomial Random Variables. Binomial Random Variables

Bernoulli Trials Definition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure. 1 Tossing a coin and considering heads as success and tails as

Chapter 8: Binomial and Geometric Distributions

Chapter 8: Binomial and Geometric Distributions Section 8.1 Binomial Distributions The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Section 8.1 Binomial Distribution Learning Objectives

Lecture 7 Random Variables

Lecture 7 Random Variables Definition: A random variable is a variable whose value is a numerical outcome of a random phenomenon, so its values are determined by chance. We shall use letters such as X

Lesson 97 - Binomial Distributions IBHL2 - SANTOWSKI

Lesson 97 - Binomial Distributions IBHL2 - SANTOWSKI Opening Exercise: Example #: (a) Use a tree diagram to answer the following: You throwing a bent coin 3 times where P(H) = / (b) THUS, find the probability

Opening Exercise: Lesson 91 - Binomial Distributions IBHL2 - SANTOWSKI

08-0- Lesson 9 - Binomial Distributions IBHL - SANTOWSKI Opening Exercise: Example #: (a) Use a tree diagram to answer the following: You throwing a bent coin times where P(H) = / (b) THUS, find the probability

Value (x) probability Example A-2: Construct a histogram for population Ψ.

Calculus 111, section 08.x The Central Limit Theorem notes by Tim Pilachowski If you haven t done it yet, go to the Math 111 page and download the handout: Central Limit Theorem supplement. Today s lecture

STOR 155 Introductory Statistics (Chap 5) Lecture 14: Sampling Distributions for Counts and Proportions

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics (Chap 5) Lecture 14: Sampling Distributions for Counts and Proportions 5/31/11 Lecture 14 1 Statistic & Its Sampling Distribution

d) Find the standard deviation of the random variable X.

Q 1: The number of students using Math lab per day is found in the distribution below. x 6 8 10 12 14 P(x) 0.15 0.3 0.35 0.1 0.1 a) Find the mean for this probability distribution. b) Find the variance

Binomial Distributions

Binomial Distributions A binomial experiment is a probability experiment that satisfies these conditions. 1. The experiment has a fixed number of trials, where each trial is independent of the other trials.

4.2 Bernoulli Trials and Binomial Distributions

Arkansas Tech University MATH 3513: Applied Statistics I Dr. Marcel B. Finan 4.2 Bernoulli Trials and Binomial Distributions A Bernoulli trial 1 is an experiment with exactly two outcomes: Success and

Probability Distributions. Definitions Discrete vs. Continuous Mean and Standard Deviation TI 83/84 Calculator Binomial Distribution

Probability Distributions Definitions Discrete vs. Continuous Mean and Standard Deviation TI 83/84 Calculator Binomial Distribution Definitions Random Variable: a variable that has a single numerical value

Random Variables CHAPTER 6.3 BINOMIAL AND GEOMETRIC RANDOM VARIABLES

Random Variables CHAPTER 6.3 BINOMIAL AND GEOMETRIC RANDOM VARIABLES Essential Question How can I determine whether the conditions for using binomial random variables are met? Binomial Settings When the

MATH 264 Problem Homework I

MATH Problem Homework I Due to December 9, 00@:0 PROBLEMS & SOLUTIONS. A student answers a multiple-choice examination question that offers four possible answers. Suppose that the probability that the

guessing Bluman, Chapter 5 2

Bluman, Chapter 5 1 guessing Suppose there is multiple choice quiz on a subject you don t know anything about. 15 th Century Russian Literature; Nuclear physics etc. You have to guess on every question.

Binomial distribution

Binomial distribution Jon Michael Gran Department of Biostatistics, UiO MF9130 Introductory course in statistics Tuesday 24.05.2010 1 / 28 Overview Binomial distribution (Aalen chapter 4, Kirkwood and

Section 8.4 The Binomial Distribution

Section 8.4 The Binomial Distribution Binomial Experiment A binomial experiment has the following properties: 1. The number of trials in the experiment is fixed. 2. There are two outcomes of each trial:

Chapter 6: Random Variables

Chapter 6: Random Variables Section 6.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 6 Random Variables 6.1 Discrete and Continuous Random Variables 6.2 Transforming and

Chapter 3 - Lecture 5 The Binomial Probability Distribution

Chapter 3 - Lecture 5 The Binomial Probability October 12th, 2009 Experiment Examples Moments and moment generating function of a Binomial Random Variable Outline Experiment Examples A binomial experiment

expl 1: Consider rolling two distinguishable, six-sided dice. Here is the sample space. Answer the questions that follow.

General Education Statistics Class Notes Conditional Probability (Section 5.4) What is the probability you get a sum of 5 on two dice? Now assume one die is a 4. Does that affect the probability the sum

The Binomial and Geometric Distributions. Chapter 8

The Binomial and Geometric Distributions Chapter 8 8.1 The Binomial Distribution A binomial experiment is statistical experiment that has the following properties: The experiment consists of n repeated

Math 243 Section 4.3 The Binomial Distribution

Math 243 Section 4.3 The Binomial Distribution Overview Notation for the mean, standard deviation and variance The Binomial Model Bernoulli Trials Notation for the mean, standard deviation and variance

Chapter. Section 4.2. Chapter 4. Larson/Farber 5 th ed 1. Chapter Outline. Discrete Probability Distributions. Section 4.

Chapter Discrete Probability s Chapter Outline 1 Probability s 2 Binomial s 3 More Discrete Probability s Copyright 2015, 2012, and 2009 Pearson Education, Inc 1 Copyright 2015, 2012, and 2009 Pearson

Lecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series

Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 5 Probability Distributions 5-1 Overview 5-2 Random Variables 5-3 Binomial Probability

S = 1,2,3, 4,5,6 occurs

Chapter 5 Discrete Probability Distributions The observations generated by different statistical experiments have the same general type of behavior. Discrete random variables associated with these experiments

Chapter 3 Discrete Random Variables and Probability Distributions

Chapter 3 Discrete Random Variables and Probability Distributions Part 3: Special Discrete Random Variable Distributions Section 3.5 Discrete Uniform Section 3.6 Bernoulli and Binomial Others sections

Probability & Statistics Chapter 5: Binomial Distribution

Probability & Statistics Chapter 5: Binomial Distribution Notes and Examples Binomial Distribution When a variable can be viewed as having only two outcomes, call them success and failure, it may be considered

Name Period AP Statistics Unit 5 Review

Name Period AP Statistics Unit 5 Review Multiple Choice 1. Jay Olshansky from the University of Chicago was quoted in Chance News as arguing that for the average life expectancy to reach 100, 18% of people

Math 361. Day 8 Binomial Random Variables pages 27 and 28 Inv Do you have ESP? Inv. 1.3 Tim or Bob?

Math 361 Day 8 Binomial Random Variables pages 27 and 28 Inv. 1.2 - Do you have ESP? Inv. 1.3 Tim or Bob? Inv. 1.1: Friend or Foe Review Is a particular study result consistent with the null model? Learning

***SECTION 8.1*** The Binomial Distributions

***SECTION 8.1*** The Binomial Distributions CHAPTER 8 ~ The Binomial and Geometric Distributions In practice, we frequently encounter random phenomenon where there are two outcomes of interest. For example,

Binomial and multinomial distribution

1-Binomial distribution Binomial and multinomial distribution The binomial probability refers to the probability that a binomial experiment results in exactly "x" successes. The probability of an event

Random variables The binomial distribution The normal distribution Sampling distributions. Distributions. Patrick Breheny.

Distributions September 17 Random variables Anything that can be measured or categorized is called a variable If the value that a variable takes on is subject to variability, then it the variable is a

Chapter 4 Discrete Random variables

Chapter 4 Discrete Random variables A is a variable that assumes numerical values associated with the random outcomes of an experiment, where only one numerical value is assigned to each sample point.

Probability Distributions

4.1 Probability Distributions Random Variables A random variable x represents a numerical value associated with each outcome of a probability distribution. A random variable is discrete if it has a finite

Experimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes

MDM 4U Probability Review Properties of Probability Experimental Probability - probability measured by performing an experiment for a number of n trials and recording the number of outcomes Theoretical

GOALS. Discrete Probability Distributions. A Distribution. What is a Probability Distribution? Probability for Dice Toss. A Probability Distribution

GOALS Discrete Probability Distributions Chapter 6 Dr. Richard Jerz Define the terms probability distribution and random variable. Distinguish between discrete and continuous probability distributions.

Discrete Probability Distributions Chapter 6 Dr. Richard Jerz

Discrete Probability Distributions Chapter 6 Dr. Richard Jerz 1 GOALS Define the terms probability distribution and random variable. Distinguish between discrete and continuous probability distributions.

CHAPTER 4 DISCRETE PROBABILITY DISTRIBUTIONS

CHAPTER 4 DISCRETE PROBABILITY DISTRIBUTIONS A random variable is the description of the outcome of an experiment in words. The verbal description of a random variable tells you how to find or calculate

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.

Math 5.3 Binomial Probability Distributions Name 1) Binomial Distrbution: Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 2) Rolling a single die

Section Random Variables

Section 6.2 - Random Variables According to the Bureau of the Census, the latest family data pertaining to family size for a small midwestern town, Nomore, is shown in Table 6.. If a family from this town

Chapter 5. Sampling Distributions

Lecture notes, Lang Wu, UBC 1 Chapter 5. Sampling Distributions 5.1. Introduction In statistical inference, we attempt to estimate an unknown population characteristic, such as the population mean, µ,

Stat 20: Intro to Probability and Statistics

Stat 20: Intro to Probability and Statistics Lecture 13: Binomial Formula Tessa L. Childers-Day UC Berkeley 14 July 2014 By the end of this lecture... You will be able to: Calculate the ways an event can

Simple Random Sample

Simple Random Sample A simple random sample (SRS) of size n consists of n elements from the population chosen in such a way that every set of n elements has an equal chance to be the sample actually selected.

Statistics 6 th Edition

Statistics 6 th Edition Chapter 5 Discrete Probability Distributions Chap 5-1 Definitions Random Variables Random Variables Discrete Random Variable Continuous Random Variable Ch. 5 Ch. 6 Chap 5-2 Discrete

Chapter 4 Discrete Random variables

Chapter 4 Discrete Random variables A is a variable that assumes numerical values associated with the random outcomes of an experiment, where only one numerical value is assigned to each sample point.

Name: Date: Pd: Review 8.3 & 8.4

Name: Date: Pd: Review 8.3 & 8.4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The histograms represent the probability distributions of the random variables

Chapter 17. The. Value Example. The Standard Error. Example The Short Cut. Classifying and Counting. Chapter 17. The.

Context Short Part V Chance Variability and Short Last time, we learned that it can be helpful to take real-life chance processes and turn them into a box model. outcome of the chance process then corresponds

Binomial Distributions

Binomial Distributions (aka Bernouli s Trials) Chapter 8 Binomial Distribution an important class of probability distributions, which occur under the following Binomial Setting (1) There is a number n

4.2 Probability Distributions

4.2 Probability Distributions Definition. A random variable is a variable whose value is a numerical outcome of a random phenomenon. The probability distribution of a random variable tells us what the

Stats SB Notes 4.2 Completed.notebook February 22, Feb 21 11:39 AM. Chapter Outline

Stats SB Notes 42 Completednotebook February 22, 2017 Chapter 4 Discrete Probability Distributions Chapter Outline 41 Probability Distributions 42 Binomial Distributions 43 More Discrete Probability Distributions

1. The data in the following table represent the number of miles per gallon achieved on the highway for compact cars for the model year 2005.

Millersville University Name Answer Key Department of Mathematics MATH 130, Elements of Statistics I, Test 2 March 5, 2010, 10:00AM-10:50AM Please answer the following questions. Your answers will be evaluated

CHAPTER 6 Random Variables

CHAPTER 6 Random Variables 6.3 Binomial and Geometric Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Binomial and Geometric Random

Probability. An intro for calculus students P= Figure 1: A normal integral

Probability An intro for calculus students.8.6.4.2 P=.87 2 3 4 Figure : A normal integral Suppose we flip a coin 2 times; what is the probability that we get more than 2 heads? Suppose we roll a six-sided

Lean Six Sigma: Training/Certification Books and Resources

Lean Si Sigma Training/Certification Books and Resources Samples from MINITAB BOOK Quality and Si Sigma Tools using MINITAB Statistical Software A complete Guide to Si Sigma DMAIC Tools using MINITAB Prof.

Chapter 12. Binomial Setting. Binomial Setting Examples

Chapter 12 Binomial Distributions BPS - 3rd Ed. Chapter 12 1 Binomial Setting Fixed number n of observations The n observations are independent Each observation falls into one of just two categories may

5.2 Random Variables, Probability Histograms and Probability Distributions

Chapter 5 5.2 Random Variables, Probability Histograms and Probability Distributions A random variable (r.v.) can be either continuous or discrete. It takes on the possible values of an experiment. It

Chapter 6: Random Variables. Ch. 6-3: Binomial and Geometric Random Variables

Chapter : Random Variables Ch. -3: Binomial and Geometric Random Variables X 0 2 3 4 5 7 8 9 0 0 P(X) 3???????? 4 4 When the same chance process is repeated several times, we are often interested in whether

Problem A Grade x P(x) To get "C" 1 or 2 must be 1 0.05469 B A 2 0.16410 3 0.27340 4 0.27340 5 0.16410 6 0.05470 7 0.00780 0.2188 0.5468 0.2266 Problem B Grade x P(x) To get "C" 1 or 2 must 1 0.31150 be

Exercises for Chapter (5)

Exercises for Chapter (5) MULTILE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) 500 families were interviewed and the number of children per family was

The Central Limit Theorem. Sec. 8.2: The Random Variable. it s Distribution. it s Distribution

The Central Limit Theorem Sec. 8.1: The Random Variable it s Distribution Sec. 8.2: The Random Variable it s Distribution X p and and How Should You Think of a Random Variable? Imagine a bag with numbers

Central Limit Theorem 11/08/2005

Central Limit Theorem 11/08/2005 A More General Central Limit Theorem Theorem. Let X 1, X 2,..., X n,... be a sequence of independent discrete random variables, and let S n = X 1 + X 2 + + X n. For each

Discrete Probability Distributions

Page 1 of 6 Discrete Probability Distributions In order to study inferential statistics, we need to combine the concepts from descriptive statistics and probability. This combination makes up the basics

CHAPTER 5 SOME DISCRETE PROBABILITY DISTRIBUTIONS. 5.2 Binomial Distributions. 5.1 Uniform Discrete Distribution

CHAPTER 5 SOME DISCRETE PROBABILITY DISTRIBUTIONS As we had discussed, there are two main types of random variables, namely, discrete random variables and continuous random variables. In this chapter,

Chapter 4 Probability Distributions

Slide 1 Chapter 4 Probability Distributions Slide 2 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5

MATH1215: Mathematical Thinking Sec. 08 Spring Worksheet 9: Solution. x P(x)

N. Name: MATH: Mathematical Thinking Sec. 08 Spring 0 Worksheet 9: Solution Problem Compute the expected value of this probability distribution: x 3 8 0 3 P(x) 0. 0.0 0.3 0. Clearly, a value is missing

Discrete Probability Distributions

Discrete Probability Distributions Chapter 6 Learning Objectives Define terms random variable and probability distribution. Distinguish between discrete and continuous probability distributions. Calculate

PROBABILITY DISTRIBUTIONS

CHAPTER 3 PROBABILITY DISTRIBUTIONS Page Contents 3.1 Introduction to Probability Distributions 51 3.2 The Normal Distribution 56 3.3 The Binomial Distribution 60 3.4 The Poisson Distribution 64 Exercise

Part 1 In which we meet the law of averages. The Law of Averages. The Expected Value & The Standard Error. Where Are We Going?

1 The Law of Averages The Expected Value & The Standard Error Where Are We Going? Sums of random numbers The law of averages Box models for generating random numbers Sums of draws: the Expected Value Standard

Binomial Random Variable - The count X of successes in a binomial setting

6.3.1 Binomial Settings and Binomial Random Variables What do the following scenarios have in common? Toss a coin 5 times. Count the number of heads. Spin a roulette wheel 8 times. Record how many times

The normal distribution is a theoretical model derived mathematically and not empirically.

Sociology 541 The Normal Distribution Probability and An Introduction to Inferential Statistics Normal Approximation The normal distribution is a theoretical model derived mathematically and not empirically.

Probability and Statistics. Copyright Cengage Learning. All rights reserved.

Probability and Statistics Copyright Cengage Learning. All rights reserved. 14.3 Binomial Probability Copyright Cengage Learning. All rights reserved. Objectives Binomial Probability The Binomial Distribution

CHAPTER 6 Random Variables

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

STA 220H1F LEC0201. Week 7: More Probability: Discrete Random Variables

STA 220H1F LEC0201 Week 7: More Probability: Discrete Random Variables Recall: A sample space for a random experiment is the set of all possible outcomes of the experiment. Random Variables A random variable

A random variable is a (typically represented by ) that has a. value, determined by, A probability distribution is a that gives the

5.2 RANDOM VARIABLES A random variable is a (typically represented by ) that has a value, determined by, for each of a. A probability distribution is a that gives the for each value of the. It is often

Shifting our focus. We were studying statistics (data, displays, sampling...) The next few lectures focus on probability (randomness) Why?

Probability Introduction Shifting our focus We were studying statistics (data, displays, sampling...) The next few lectures focus on probability (randomness) Why? What is Probability? Probability is used

Discrete Probability Distributions

Discrete Probability Distributions Chapter 6 McGraw-Hill/Irwin Copyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Learning Objectives LO1 Identify the characteristics of a probability

Chapter 6 Probability

Chapter 6 Probability Learning Objectives 1. Simulate simple experiments and compute empirical probabilities. 2. Compute both theoretical and empirical probabilities. 3. Apply the rules of probability

The Binomial distribution

The Binomial distribution Examples and Definition Binomial Model (an experiment ) 1 A series of n independent trials is conducted. 2 Each trial results in a binary outcome (one is labeled success the other

4: Probability. Notes: Range of possible probabilities: Probabilities can be no less than 0% and no more than 100% (of course).

4: Probability What is probability? The probability of an event is its relative frequency (proportion) in the population. An event that happens half the time (such as a head showing up on the flip of a

3. The n observations are independent. Knowing the result of one observation tells you nothing about the other observations.

Binomial and Geometric Distributions - Terms and Formulas Binomial Experiments - experiments having all four conditions: 1. Each observation falls into one of two categories we call them success or failure.

Section 6.3 Binomial and Geometric Random Variables

Section 6.3 Binomial and Geometric Random Variables Mrs. Daniel AP Stats Binomial Settings A binomial setting arises when we perform several independent trials of the same chance process and record the

Example. Chapter 8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables

Chapter 8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables You are dealt a hand of 5 cards. Find the probability distribution table for the number of hearts. Graph

Section 8.4 The Binomial Distribution. (a) Rolling a fair die 20 times and observing how many heads appear. s

Section 8.4 The Binomial Distribution Binomial Experiment A binomial experiment has the following properties: 1. The number of trials in the experiment is fixed. 2. There are two outcomes of each trial:

STA Module 3B Discrete Random Variables

STA 2023 Module 3B Discrete Random Variables Learning Objectives Upon completing this module, you should be able to 1. Determine the probability distribution of a discrete random variable. 2. Construct

The Binomial Distribution

The Binomial Distribution Patrick Breheny February 16 Patrick Breheny STA 580: Biostatistics I 1/38 Random variables The Binomial Distribution Random variables The binomial coefficients The binomial distribution

We use probability distributions to represent the distribution of a discrete random variable.

Now we focus on discrete random variables. We will look at these in general, including calculating the mean and standard deviation. Then we will look more in depth at binomial random variables which are