# Introduction to Probability and Statistics -Year 2022

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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.
###### 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 variables

Discrete versus Continuous Variables

Summary of Types of Variables

• Frequency Table
• Relative Class Frequencies
• Bar Charts
• Frequency DistributionEXAMPLE – 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
• 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 Median

EXAMPLES – Median

• The ModeExample – Mode
• The Relative Positions of the Mean, Median and the Mode

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 #1

Solve the above example by theorem.

Permutation Examples

Permutation Theorem #2

• CombinationExamples
• Difference between permutation & combination
• DefinitionsExperiment

Outcome

Event

• Classical ProbabilityExamples
• Mutually Exclusive and Independent Events
• Empirical ProbabilityExample
• Complement RuleExample

Lecture 5

• Conditional ProbabilityFormulae

Examples

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

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