GNE 331 – LAU Package 1
August 30, 2021 20210913 8:04GNE 331 – LAU Package 1
GNE 331 – LAU Package 1
Probability and Statistics is a course that equips you with the necessary tools for making wise decisions in the face of uncertainty.
In section 1, you will learn the difference between a population and a sample, as well as the difference between descriptive and inferential statistics. In this chapter we focus on descriptive statistics and the various methods we can use to organize and display data that we collect from a sample in an attempt to draw conclusions about the whole population. You will learn how to organize the data into frequency and relative frequency distribution tables, and how to use these tables to display the data on bar graphs, histograms, pie charts, and boxplots. Moreover, you will learn how to calculate measures of center and measures of variability that statisticians use as sample representatives.
In section 2, we recall important definitions from set theory that we will use extensively for counting and probability. We learn the meaning of probability, sample space, events and relationships between events. We also learn how to use Venn Diagrams and Tree Diagrams to simplify problems. Finally, we learn the concept of independence of events as well as conditional probability.
In section 3, we learn the various techniques we can use to count the number of elements in a given set. We learn the multiplication rule for counting, the use of factorials, permutations and combinations. We also learn an extra bunch of problemspecific counting techniques such as permutations involving fixing positions and/or fixing order.
In section 4, we define a random variable and its two types (discrete and continuous). We also define probability mass functions, cumulative distribution functions, expected value and variance. Furthermore, We dig deeper into discrete random variables and their distributions: Bernoulli distribution, Binomial distribution, Hypergeometric distribution, geometric distribution, negative binomial distribution, and Poisson distribution.

Section 1: Descriptive Statistics
In this section we give an overview on probability and statistics. Here you will learn how to conduct the first part of any statistical research: Organizing and visualizing data through histograms, pie charts, boxplots and bar graphs. Moreover, you will learn about the measures of center and variability and how to calculate them.
 Lesson 1: Population Versus Sample
 Lesson 2: Descriptive and Inferential Statistics
 Lesson 3: Frequency and Relative Frequency
 Lesson 4: Qualitative Data and Bar Graphs
 Lesson 5: Quantitative Data (SingleValued Tables)

Lesson 6: Quantitative Data (Class Intervals)

Lesson 7: Histograms and Polygons

Lesson 8: Cumulative Frequency Distribution Tables

Lesson 9: Stem and Leaf Displays

Problem 1

Problem 2

Problem 3

Lesson 10: Measures of Center

Problem 4

Lesson 11: Symmetric And Skewed Histograms

Lesson 12: Measures of Variability

Lesson 13: Variance and Standard Deviation

Problem 5

Lesson 14: Trimmed Mean

Lesson 15: Quartiles

Lesson 16: Percentiles

Lesson 17: Interquartile Range (IQR) and Outliers

Problem 6

Problem 7

Lesson 18: Boxplot

Problem 8

Quiz 1

Quiz 1 Solution

Quiz 2

Quiz 2 Solution

Section 2: Sample Space, Events, and Set Theory
In this section, we review some important concepts from set theory (sets, events, and their relationships). We also define probability, conditional probability, and the concept of independence of events.
 Lesson 1: Probability, Sample Space, and Events

Lesson 2: Relationships Between Events

Lesson 3: Venn Diagram

Lesson 4: Axioms, Interpretation, and Properties of Probability

Lesson 5: Conditional Probability

Lesson 6: Tree Diagram

Lesson 7: Baye’s Theorem and Independence of Events

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Quiz 1

Quiz 1 Solution

Quiz 2

Quiz 2 Solution

Section 3: Counting Techniques
In this section, you learn various counting techniques that will help you determine the number of elements in a given set. You will use the concepts discussed in this chapter to count the number of elements in the sample space and the event under study and use them to find probabilities of events.
 Lesson 1: Multiplication Rule

Lesson 2: Factorials

Lesson 3: Permutations and Combinations

Problem 1

Lesson 4: Fixing Positions

Lesson 5: Fixing Order

Lesson 6: Distributing “n” indistinguishable balls into “k” distinguishable boxes

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Quiz 1

Quiz 1 Solution

Quiz 2

Quiz 2 Solution

Mock Exams (Sections 13)
Below you will find mock exams that cover all the concepts explained in this package.

Mock Exam 1 – Sections 1, 2 and 3

Mock Exam 1 Solution


Section 4: Discrete Probability Distributions
In this section we define a random variable and its two types: discrete and continuous random variables. Furthermore, we dig deeper into discrete random variables and their probability distributions.
 Lesson 1: Discrete and Continuous Random Variables

Lesson 2: Discrete pmfs, Expected Value, and Variance

Lesson 3: E(g(x)) and Var(g(x))

Lesson 4: Cumulative Distribution Function in Discrete Random Variables

Lesson 5: pdf to cdf and cdf to pdf

Quiz 1

Quiz 1 Solution

Lesson 6: Bernoulli Distribution

Lesson 7: Binomial Distribution

Lesson 8: Cumulative Distribution Function for Binomial Experiment

Table 1: Cumulative Distribution Tables for the Binomial Distribution

Quiz 2

Quiz 2 Solution

Lesson 9: Hypergeometric Distribution

Lesson 10: Geometric Distribution

Lesson 11: Negative Binomial Distribution

Quiz 3

Quiz 3 Solution

Lesson 12: Poisson Distribution

Lesson 13: Cumulative Distribution Table for Poisson Distribution

Problem 1

Table 2: Cumulative Distribution Tables for the Poisson Distribution

Quiz 4

Quiz 4 Solution

Lesson 14: Approximating Hypergeometric Distribution by Binomial Distribution

Lesson 15: Approximating Binomial Distribution by Binomial Distribution