Introduction to Probability and Statistics -Year 2022

Reference Books & Course Outline

Lecture 1-Part 2

Outline

• 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

Learning Objectives

1. Understand why we study statistics.

2. Explain what is meant by descriptive statistics and inferential statistics.

3. Distinguish between a qualitative variable and a quantitative variable.

4. Describe how a discrete variable is different from a continuous variable.

Lecture 1-Part 2

Outline

• 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

Learning Objectives

1. Organize qualitative data into a frequency table.

2. Present a frequency table as a bar chart.

3. Organize quantitative data into a frequency distribution.

4. Present a frequency distribution for quantitative data using histograms, frequency polygons, and cumulative frequency polygons.

Lecture 2-Part 1

Outline

• 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

Learning Objectives

  1· Calculate the arithmetic mean, median, mode, and geometric mean.

  2· Explain the characteristics, uses, advantages, and disadvantages of each measure of location.

  3· Identify the position of the mean, median, and mode for both symmetric and skewed distributions.

Lecture 2-Part 2

Outline

• 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

Learning Objectives

1· Compute and interpret the range, mean deviation, variance, and standard deviation.

2· Understand the characteristics, uses, advantages, and disadvantages of each measure of dispersion.

3· Understand Chebyshev’s theorem and the Empirical Rule as they relate to a set of observations.

Lecture 3-Part 1

Outline

• 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.

Learning Objectives

1. Understand how to find mean, median and mode for the group data.

Lecture 3-Part 2

Outline

• Finding the Variance & Standard Deviation for Grouped Data

  Examples

• Skewness

  Examples

• Pearson coefficient of Skewness (PC)

  Examples

Learning Objective

1. Understand Skewness and Pearson Coefficient of Skewness for group data.

Lecture 4-Part 1

Outline

• Permutation

  Permutation Theorem #1

  Solve above example by theorem.

  Permutation Examples

  Permutation Theorem #2

• Combination

  Examples

Learning Objectives

1. Define Permutation and Combination

2. Understand the Permutation Theorems with the help of examples

Lecture 4-Part 2

Outline

• 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

Learning Objectives

1. Describe the classical, empirical, and subjective approaches to probability.

2. Explain the terms experiment, event, outcome, permutations, and combinations.

Lecture 5-Part 1

Outline

• Conditional Probability

  Formulae

  Examples

• Special Rule for Multiplication

  Example

Learning Objectives

1. Define the terms conditional probability and joint probability.

2. Calculate probabilities using the rules of addition and rules of multiplication.

Lecture 5-Part 2

Outline

• General Rule for Multiplication

  Example

• Contingency Table

  Example

• Generalized Conditional Probability

  Example

• Bayes’ rule for conditional probability

  Example

Learning Objectives

1. Understand General rules for Multiplication.

2. Conditional probability and Beye’s rule of conditional probability.

Lecture 6-Part 1

Outline

• 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

Leaning Objectives

1. Define the terms probability distribution and random variable.

2. Distinguish between discrete and continuous probability distributions.

3. Calculate the mean, variance, and standard deviation of a discrete probability distribution.

Lecture 6-Part 2

• Discrete Probability Distribution

  Binomial Probability Distribution.

  Example

  Poisson Probability Distribution.

  Example

  -ve binomial and Geometric Probability Distribution

  Example

Learning Objectives

1. Describe the characteristics of and compute probabilities using the binomial probability distribution.

2. Describe the characteristics of and compute probabilities using the Poisson probability distribution

3. Describe the characteristics of and compute probabilities using the –ve binomial and geometric probability distribution.

Lecture 7- Part 1

• Probability density function (pdf)

  Properties of pdf

  Example

Learning Objectives

1. Understand the difference between discrete and continuous distributions.

2. Understand probability density function with properties and function.

Lecture 7- Part 2

Outline

• Cumulative distribution function (cdf)

  Properties of cdf

  Example

Learning Objectives

1. CDF of continuous Probability Distribution.

2. Application CDF

Lecture 7- Part 3

Outline

• The Family of Uniform Distributions

• The Uniform Distribution

  Mean and Standard Deviation

  Examples

Learning Objectives

1. Compute the mean and the standard deviation for a uniform distribution.

2. Compute probabilities by using the uniform distribution.

Lecture 8-Part 1

Outline

• 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

Learning Objectives

1. List the characteristics of the normal probability distribution.

2. Define and calculate z values.

3. Determine the probability an observation is between two points on a normal probability distribution.

4. Determine the probability an observation is above (or below) a point on a normal probability distribution.

Lecture 8-Part 2

Outline

• 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

Learning Objectives

1. Concept of Simple Linear Regression

2. Understand the Regression Model

3. Estimated Regression Equation

4. Regression Example

5. Coefficient of Determination

Lecture 9-Part 1

Outline

• Correlation

  Examples

Learning Objectives

1. Coefficient of Correlation

Lecture 9-Part 2

Outline

• Hypothesis

  What is Hypothesis Testing?

  Hypothesis Testing Steps

• Null and alternative hypothesis

• One and Two tailed test

Learning Objectives

1. Define a hypothesis and hypothesis testing.

2. Describe the six-step hypothesis-testing procedure.

3. Distinguish between a one-tailed and a two-tailed test of hypothesis.

4. Conduct a test of hypothesis about a population mean.