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