Probability And Statistics For Undergraduate Students

Foundations of Probability and Statistics for STEM Students and Engineers

What you'll learn

Master basic probability concepts, including conditional probability and Bayes’ Theorem.

Use descriptive statistics to summarize and analyze data.

Work with key distributions: Binomial, Poisson, and Normal.

Perform hypothesis tests and calculate confidence intervals.

Solve real-world STEM problems using statistics.

Build data interpretation and critical thinking skills.

Requirements

A basic understanding of algebra

Interest in STEM fields like engineering, science, or computer science

No prior knowledge of statistics or probability is required

A calculator (scientific or graphing) is recommended for practice problems

Description

Unlock the fundamentals of Probability and Statistics with this comprehensive course designed specifically for STEM undergraduates and aspiring engineers. Whether you’re preparing for exams like the FE, enhancing your analytical skills, or building a strong foundation in data analysis and probability theory, this course offers everything you need.Starting with basic concepts such as probability rules and descriptive statistics, the course advances to key topics including discrete and continuous probability distributions, sampling methods, and hypothesis testing. You’ll develop the ability to interpret data, assess uncertainty, and make informed decisions based on statistical reasoning—skills crucial in engineering, computer science, physics, biology, and other STEM fields.What You’ll Learn:Understand core probability concepts including conditional probability and Bayes’ Theorem.Summarize and analyze data using descriptive statistics and visualization techniques.Work with important distributions like Binomial, Poisson, and Normal to model real-world phenomena.Perform hypothesis testing and construct confidence intervals to support decision making.Apply statistical methods to solve practical problems relevant to STEM careers and research.What’s Included:Over 120 engaging video lectures with clear explanations and real-world examples.Interactive quizzes and practice problems to reinforce your learning.Step-by-step walkthroughs of probability and statistics problems common in exams and professional work.This course is perfect for:Undergraduate STEM students in engineering, computer science, physics, mathematics, and related fields.Students preparing for the FE exam or other professional certification tests.Anyone seeking to strengthen their statistical reasoning and data analysis skills.With hands-on problem-solving and accessible teaching, this course will equip you with the confidence to tackle statistics challenges in your academic and professional journey. Enroll today and build a strong foundation in Probability and Statistics!

Overview

Section 1: Descriptive Statistics

Lecture 1 Population Versus Sample

Lecture 2 Descriptive and Inferential Statistics

Lecture 3 Frequency and Relative Frequency

Lecture 4 Qualitative Data and Bar Graphs

Lecture 5 Quantitative Data (Single-Valued Tables)

Lecture 6 Quantitative Data (Class Intervals)

Lecture 7 Histograms and Polygons

Lecture 8 Cumulative Frequency Distribution Tables

Lecture 9 Stem and Leaf Displays

Lecture 10 Problem Solving Session 1

Lecture 11 Problem Solving Session 2

Lecture 12 Problem Solving Session 3

Lecture 13 Measures of Center

Lecture 14 Problem Solving Session 4

Lecture 15 Symmetric And Skewed Histograms

Lecture 16 Measures of Variability

Lecture 17 Variance and Standard Deviation

Lecture 18 Problem Solving Session 5

Lecture 19 Trimmed Mean

Lecture 20 Quartiles

Lecture 21 Percentiles

Lecture 22 Interquartile Range (IQR) and Outliers

Lecture 23 Problem Solving Session 6

Lecture 24 Problem Solving Session 7

Lecture 25 BoxPlot

Lecture 26 Problem Solving Session 8

Section 2: Sample Space, Events, and Set Theory

Lecture 27 Sample Space and Probability of Events

Lecture 28 Relationships Between Sets

Lecture 29 Venn Diagram

Lecture 30 Axioms and Properties

Lecture 31 Conditional Probability

Lecture 32 Bayes' Theorem

Lecture 33 Tree Diagram

Lecture 34 Problem 1

Lecture 35 Problem 2

Lecture 36 Problem 3

Lecture 37 Problem 4

Lecture 38 Problem 5

Lecture 39 Problem 6

Section 3: Counting Techniques

Lecture 40 Multiplication Rule

Lecture 41 Factorials

Lecture 42 Permutations and Combinations

Lecture 43 Problem 1

Lecture 44 Fixing Positions

Lecture 45 Fixing Order

Lecture 46 Distributing Indistinguishable Balls into Distinguishable Boxes

Lecture 47 Problem 2

Lecture 48 Problem 3

Lecture 49 Problem 4

Lecture 50 Problem 5

Lecture 51 Problem 6

Section 4: Discrete Probability Distributions

Lecture 52 Discrete and Continuous Random Variables

Lecture 53 Discrete Probability Mass Function, Expected Value, and Variance

Lecture 54 Expected Value and Variance of Functions of x

Lecture 55 Cumulative Distribution Functions

Lecture 56 Probability Density Functions and Cumulative Density Functions

Lecture 57 The Bernoulli Distribution

Lecture 58 The Binomial Distribution

Lecture 59 Cumulative Distribution Table of the Binomial Distribution

Lecture 60 The Hypergeometric Distribution

Lecture 61 The Geometric Distribution

Lecture 62 The Negative Binomial Distribution

Lecture 63 The Poisson Distribution

Lecture 64 Cumulative Distribution table of the Poisson Distribution

Lecture 65 Approximating the Hypergeometric Distribution with the Binomial Distribution

Lecture 66 Approximating the Binomial Distribution by the Poisson Distribution

Lecture 67 Problem 1

Section 5: Continuous Probability Distributions

Lecture 68 Probability Density Function for Continuous Random Variables

Lecture 69 Problem 1

Lecture 70 Expected Value and Variance

Lecture 71 Cumulative Distribution Function

Lecture 72 Problem 2

Lecture 73 Continuous Probability Distributions

Lecture 74 The Uniform Distribution

Lecture 75 The Normal Distribution

Lecture 76 The Standard Normal Distribution Curve

Lecture 77 From X to Z

Lecture 78 The Exponential Distribution

Lecture 79 The Memoryless Property

Lecture 80 Exponentials in a Poisson Process

Lecture 81 The Gamma Distribution

Lecture 82 The Incomplete Gamma Function

Lecture 83 The Chi Squared Distribution

Lecture 84 Approximating the Binomial Distribution by the Normal Distribution

Lecture 85 From on Probability Density Function to Another

Section 6: Joint Probability Distributions of Two Random Variables

Lecture 86 Introduction to Joint Probability Distribution

Lecture 87 Joint Probability Mass Function in Two Discrete Random Variables

Lecture 88 Expected Value of a Function of Two Discrete Random Variables

Lecture 89 Covariance and Linear Relationship

Lecture 90 Correlation of Two Random Variables

Lecture 91 Independence of Two Discrete Random Variables

Lecture 92 Introduction to Joint Probability Density Function of Two Continuous Random Vars

Lecture 93 Problem 1: Review on Double Integrals

Lecture 94 Problem 2: Review on Double Integrals

Lecture 95 Marginal pdf in Two Continuous Random Variables

Lecture 96 Expected Value of a Function of Two Continuous Random Variables

Lecture 97 Problem 3

Lecture 98 Problem 4

Lecture 99 Problem 5

Lecture 100 Problem 6

Lecture 101 Problem 7

Lecture 102 Conditional Pmf and Conditional Pdf

Lecture 103 Conditional Expectations

Lecture 104 Expected Value and Variance of Linear Combination

Section 7: Sampling Distributions

Lecture 105 Introduction to Sampling Distributions

Lecture 106 Sampling Distribution of the Sample Mean for Normal Population

Lecture 107 Central Limit Theorem

Lecture 108 Sampling Distribution of Sample Proportion

Lecture 109 Sampling Distribution of Sample Variance

Section 8: Confidence Intervals

Lecture 110 Point Estimates

Lecture 111 Biased and Unbiased Estimators

Lecture 112 Standard Error of the Estimate

Lecture 113 Method of Moments

Lecture 114 Introduction to Confidence Intervals

Lecture 115 Confidence Intervals for Population Mean with Known Standard Deviation

Lecture 116 Margin of Error, Width, and Sample Size

Lecture 117 T-Distribution

Lecture 118 T-Tables

Lecture 119 Confidence Interval for Population Mean with Unknown Sigma (n<40)

Lecture 120 Confidence Interval for Population Mean with Unknown Sigma (n>40)

Lecture 121 Summary

Lecture 122 Problem 1

Lecture 123 Confidence Interval for Population Proportion

Lecture 124 Confidence Interval for Population Variance

Lecture 125 Problem 2

Section 9: Hypothesis Testing

Lecture 126 Null and Alternative Hypothesis

Lecture 127 Types of Errors

Lecture 128 Critical Value Approach

Lecture 129 Critical Value Approach with Unknown Sigma

Lecture 130 Critical Value Approach For p When Binomial is Approximately Normal

Lecture 131 Critical Value Approach For p When Binomial is NOT Approximately Normal

Lecture 132 Critical Value Approach For Population Variance

Lecture 133 P-value Approach for Population Mean with Known Sigma

Lecture 134 P-value Approach for Population Mean with Unknown Sigma

Lecture 135 P-value Approach for p with Normal Approximation

Lecture 136 P-value Approach for p without Normal Approximation

Lecture 137 P-value Approach for Population Variance

This course is designed for undergraduate students in STEM majors—including engineering, computer science, physics, biology, and mathematics—who want a solid foundation in probability and statistics. It’s also ideal for students preparing for the FE exam or anyone looking to strengthen their skills for data-driven problem solving. No prior statistics background is required.