Introduction to Probability and Statistics for the year 2022

16 Hours Course especially designed for the University Students who want to become Expert from very Basics Level.

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.
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

Elementary Statistics by ALAN G. BLUMAN.(8th Edition)

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.

Variables

Types of variables

Discrete versus Continuous Variables

Summary of Types of Variables

Frequency Table

Relative Class Frequencies

Bar Charts

Frequency Distribution

EXAMPLE – Constructing Frequency Distributions: Quantitative Data

Constructing a Frequency Table - Example

Class Intervals and Midpoints with Examples

Relative Frequency Distribution

Graphic Presentation of a Frequency Distribution

Histogram

Histogram Using Excel

Frequency Polygon

Cumulative Frequency Distribution

Lecture 2

Numerical Descriptive Measures (Measures of location and dispersion)

Central Tendency

Population Mean

EXAMPLE – Population Mean

Sample Mean

EXAMPLE – Sample Mean

Properties of the Arithmetic Mean

The Median

Properties of the Median

EXAMPLES - Median

The Mode

Example – Mode

The Relative Positions of the Mean, Median and the Mode

The Geometric Mean

EXAMPLE – Geometric Mean

DISPERSION

Samples of Dispersions

Types of Dispersion

Examples

Range

Mean Deviation

Variance and Standard Deviation

Sample Variance

The Empirical Rule

Coefficient of Variance (C.V)

Examples

Lecture 3

Coefficient of Variance (C.V)

Example

Mean

Finding the Mean for group data

Median

Finding the Median for group data.

Mode

Finding the Mode for group data.

Finding the Variance & Standard Deviation for Grouped Data

Examples

Skewness

Examples

Pearson coefficient of Skewness (PC)

Examples

Lecture 4

Permutation

Permutation Theorem #1

Solve the above example by theorem.

Permutation Examples

Permutation Theorem #2

Combination

Examples

Difference between permutation & combination

Definitions

Experiment

Outcome

Event

Classical Probability

Examples

Mutually Exclusive and Independent Events

Empirical Probability

Example

Addition Rule

Example

Complement Rule

Example

Lecture 5

Conditional Probability

Formulae

Examples

Special Rule for Multiplication

Example

General Rule for Multiplication

Example

Contingency Table

Example

Generalized Conditional Probability

Example

Bayes’ rule for conditional probability

Example

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 Variables

Types of Random Variables

Discrete Random Variables – Examples

Continuous Random Variables - Examples

Prob. Mass function (pmf)

Probability Distribution

The Mean of a Discrete Probability Distribution

The Variance, and Standard Deviation of a Discrete Probability Distribution

Mean, Variance, and Standard Deviation of a Discrete Probability Distribution – Example

Mean of a Discrete Probability Distribution - Example

Variance and Standard Deviation of a Discrete Probability Distribution – Example

Discrete Probability Distribution

Binomial Probability Distribution.

Example

Poisson Probability Distribution.

Example

-ve binomial and Geometric Probability Distribution

Example

Lecture 7

Probability density function (PDF)

Properties of PDF

Example

Cumulative distribution function (CDF)

Properties of CDF

Example

The Family of Uniform Distributions

The Uniform Distribution

Mean and Standard Deviation

Examples

Lecture 8

Normal probability distribution

Examples

Characteristics of a Normal Probability Distribution

The Normal Distribution – Graphically

The Normal Distribution – Families

The Standard Normal Probability Distribution

Areas Under the Normal Curve

Z-TABLE

The Empirical Rule

Normal Distribution – Finding Probabilities

Examples

Using Z in Finding X Given Area –

Examples

Alternate Method

Simple Linear Regression

Simple Linear Regression Model

Graph

Simple Linear Regression Equation

Positive, Negative and Non Relationship

Estimation Process

Least Squares Method

Y-Intercept for the Estimated Regression Equation

Lecture 9

Correlation

Examples

Hypothesis

What 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 Deviation

Examples

Estimation and Confidence Intervals

Interval Estimates

Factors Affecting Confidence Interval Estimates

Confidence Interval Estimates for the Mean

When to Use the z or t Distribution for Confidence Interval Computation

Confidence Interval for the Mean – Example using the t-distribution

Student’s t-distribution Table

Two-sample Tests of Hypothesis

Comparing two populations

Comparing two populations (Mean of Independent Samples)

Comparing Population Means with Unknown Population Standard Deviations (the Pooled t-test)

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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