# Introduction to Probability and Statistics -Year 2022

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## Description

In this course, everything has been broken down into a simple structure to make learning and understanding easy for you.

Probability and statistics help to bring logic to a world replete with randomness and uncertainty. This course will give you the tools needed to understand data, science, philosophy, engineering, economics, and finance. You will learn not only how to solve challenging technical problems, but also how you can apply those solutions in everyday life and can solve many problems from the books for your exams.

With examples from our daily life and and from the famous books on these topics, you will gain a strong foundation for the study of statistical inference, stochastic processes, randomized algorithms, and other subjects where probability is needed.

As this course is specially designed for the University and High School Students who are facing difficulties in their studies and for those who want to boost up their skills in this field.

With this 16 Hours Probability and Statistics course,you can understand from very basic level and can become expert in this course.

Textbooks used for this course

1. Elementary Statistics by ALAN G. BLUMAN.(8th Edition)
2. Probability and Statistics for Engineers and Scientists by WALPOLE & MYERS YE.(9th Edition)

Lecture 1

• What is meant by Statistics?
• Formal Definition of Statistics and types of Statistics.
• Uses of Statistics?
• Population versus Sample.Why take a sample instead of studying every member of the population?Usefulness of a Sample in learning about a Population.
• VariablesTypes of variablesDiscrete versus Continuous VariablesSummary of Types of Variables
• Frequency Table
• Relative Class Frequencies
• Bar Charts
• Frequency DistributionEXAMPLE – Constructing Frequency Distributions: Quantitative DataConstructing a Frequency Table – Example
• Class Intervals and Midpoints with Examples
• Relative Frequency Distribution
• Graphic Presentation of a Frequency Distribution
• HistogramHistogram Using Excel
• Frequency Polygon
• Cumulative Frequency Distribution

Lecture 2

• Numerical Descriptive Measures (Measures of location and dispersion)
• Central Tendency
• Population MeanEXAMPLE – Population Mean
• Sample MeanEXAMPLE – Sample Mean
• Properties of the Arithmetic Mean
• The MedianProperties of the MedianEXAMPLES – Median
• The ModeExample – Mode
• The Relative Positions of the Mean, Median and the Mode
• The Geometric MeanEXAMPLE – Geometric Mean
• DISPERSIONSamples of DispersionsTypes of Dispersion
• ExamplesRangeMean DeviationVariance and Standard DeviationSample Variance
• The Empirical Rule
• Coefficient of Variance (C.V)Examples

Lecture 3

• Coefficient of Variance (C.V)Example
• MeanFinding the Mean for group data
• MedianFinding the Median for group data.
• ModeFinding the Mode for group data.
• Finding the Variance & Standard Deviation for Grouped DataExamples
• SkewnessExamples
• Pearson coefficient of Skewness (PC)Examples

Lecture 4

• PermutationPermutation Theorem #1Solve the above example by theorem.Permutation ExamplesPermutation Theorem #2
• CombinationExamples
• Difference between permutation & combination
• DefinitionsExperimentOutcomeEvent
• Classical ProbabilityExamples
• Mutually Exclusive and Independent Events
• Empirical ProbabilityExample
• Complement RuleExample

Lecture 5

• Conditional ProbabilityFormulaeExamples
• Special Rule for MultiplicationExample
• General Rule for MultiplicationExample
• Contingency TableExample
• Generalized Conditional ProbabilityExample
• Bayes’ rule for conditional probabilityExample

Lecture 6

• What is a Probability Distribution?
• Probability Distribution of Number of Heads Observed in 3 Tosses of a Coin
• Characteristics of a Probability Distribution
• Random VariablesTypes of Random VariablesDiscrete Random Variables – ExamplesContinuous Random Variables – Examples
• Prob. Mass function (pmf)
• Probability DistributionThe Mean of a Discrete Probability DistributionThe Variance, and Standard Deviation of a Discrete Probability DistributionMean, Variance, and Standard Deviation of a Discrete Probability Distribution – ExampleMean of a Discrete Probability Distribution – ExampleVariance and Standard Deviation of a Discrete Probability Distribution – Example
• Discrete Probability DistributionBinomial Probability Distribution.ExamplePoisson Probability Distribution.Example-ve binomial and Geometric Probability DistributionExample

Lecture 7

• Probability density function (PDF)Properties of PDFExample
• Cumulative distribution function (CDF)Properties of CDFExample
• The Family of Uniform Distributions
• The Uniform DistributionMean and Standard DeviationExamples

Lecture 8

• Normal probability distributionExamplesCharacteristics of a Normal Probability DistributionThe Normal Distribution – GraphicallyThe Normal Distribution – FamiliesThe Standard Normal Probability Distribution
• Areas Under the Normal Curve
• Z-TABLE
• The Empirical Rule
• Normal Distribution – Finding ProbabilitiesExamples
• Using Z in Finding X Given Area –Examples
• Alternate Method
• Simple Linear Regression
• Simple Linear Regression ModelGraph
• Simple Linear Regression EquationPositive, Negative and Non Relationship
• Estimation Process
• Least Squares MethodY-Intercept for the Estimated Regression Equation

Lecture 9

• CorrelationExamples
• HypothesisWhat is Hypothesis Testing?Hypothesis Testing Steps
• The null and alternative hypothesis
• One and Two-tailed test

Lecture 10

• Important Things to Remember about H0 and H1
• Left-tail or Right-tail Test?
• Parts of a Distribution in Hypothesis Testing
• One-tail vs. Two-tail Test
• Test of Single POP Mean (σ Unknown)Test 1 and Test 2
• Testing for a Population Mean with a Known Population Standard DeviationExamples
• Estimation and Confidence Intervals
• Interval EstimatesFactors Affecting Confidence Interval EstimatesConfidence Interval Estimates for the MeanWhen to Use the z or t Distribution for Confidence Interval ComputationConfidence Interval for the Mean – Example using the t-distribution
• Student’s t-distribution Table
• Two-sample Tests of HypothesisComparing two populationsComparing two populations (Mean of Independent Samples)Comparing Population Means with Unknown Population Standard Deviations (the Pooled t-test)

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## What you’ll learn

• Understand why we study statistics.
• Explain what is meant by descriptive statistics and inferential statistics.
• Distinguish between a qualitative variable and a quantitative variable
• Describe how a discrete variable is different from a continuous variable.
• Organize qualitative data into a frequency table.
• Present a frequency table as a bar chart.
• Organize quantitative data into a frequency distribution.
• Present a frequency distribution for quantitative data using histograms, frequency polygons, and cumulative frequency polygons.
• Calculate the arithmetic mean, median, mode, and geometric mean.
• Explain the characteristics, uses, advantages, and disadvantages of each measure of location.
• Identify the position of the mean, median, and mode for both symmetric and skewed distributions.
• Compute and interpret the range, mean deviation, variance, and standard deviation.
• Understand the characteristics, uses, advantages, and disadvantages of each measure of dispersion.
• Understand Chebyshev’s theorem and the Empirical Rule as they relate to a set of observations.
• Understand Skewness and Pearson Coefficient of Skewness for group data.
• Define Permutation and Combination and Understand the Permutation Theorems with the help of examples.
• Describe the classical, empirical, and subjective approaches to probability.
• Explain the terms experiment, event, outcome, permutations, and combinations.
• Define the terms conditional probability and joint probability.
• Calculate probabilities using the rules of addition and rules of multiplication.
• Understand General rules for Multiplication and Conditional probability and Beye’s rule of conditional probability.
• Understand Probability Distribution and Characteristics of a Probability Distribution.
• Random Variables and Types of Random Variables ( Discrete Random Variables – Examples Continuous Random Variables – Examples )
• Understand Probability Mass function (pmf)
• Distinguish between discrete and continuous probability distributions.
• Calculate the mean, variance, and standard deviation of a discrete probability distribution.
• Describe the characteristics of and compute probabilities using the binomial ,Poisson,–ve binomial and geometric probability distribution.
• Understand probability density function (PDF) with properties, function and examples.
• Understand Cumulative distribution function (CDF) and Properties and Applications of CDF with Example
• List the characteristics of the normal probability distribution.
• Define and calculate z values.
• Determine the probability an observation is between two points on a normal probability distribution.
• Determine the probability an observation is above (or below) a point on a normal probability distribution.
• Concept of Simple Linear Regression (Regression Model, Estimated Regression Equation, Regression Example,)
• Coefficient of Determination andCoefficient of Correlation.
• Define a hypothesis and hypothesis testing with six-step hypothesis-testing procedure.
• Distinguish between a one-tailed and a two-tailed test of hypothesis.
• Conduct a test of hypothesis about a population mean.

## Requirements

• Knowledge of basic algebra and comfortable with basic arithmetic (addition, subtraction, multiplication, division) of whole numbers.
• All concepts are introduced slowly and gradually, but comfort with thinking analytically will be helpful.

## Who this course is for:

• Business Analysts/ Managers who want to expand on the current set of skills
• Students that are taking or would like to take an introductory course in Statistics in college or an AP course in high school will find this course useful.
• Current probability and statistics students, or students about to start probability and statistics who are looking to get ahead
• Anyone curious to master Probability and Statistics in a short span of time
• Home school parents looking for extra support with probability and statistics
• Anyone who wants to study math for fun after being away from school for a while
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