Patrick J

Hypothesis Testing for a Normal Distribution, Sigma Known

8K views · 1y ago · 7:55

Here we look at a quick example of conducting a hypothesis test. In this video, we'll walk you through a step-by-step process for testing hypotheses with a known normal distribution. Using a real-world example, you'll learn how to set up null and alternative hypotheses, calculate the test statistic, and use the rejection region approach as well as the p-value approach to decide whether or not to reject the null hypothesis.

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Constructing Confidence Intervals

3K views · 1y ago · 6:31

Introduction to Hypothesis Testing

1K views · 1y ago · 5:15

In this video I look at a quick intro to hypothesis testing. I try to give some motivation as well as highlight some important formulas for future reference.

Performing a Hypothesis Test, Sigma Known

1K views · 1y ago · 7:45

Understanding Confidence Intervals | How to Construct and Interpret Them in Statistics

5K views · 1y ago · 7:21

Guest: Understanding Confidence Intervals

In this video, we break down the concept of confidence intervals—a fundamental topic in statistics that helps you estimate a range for a population parameter. Using real-world examples, we explore how to calculate and interpret confidence intervals step by step, using sample data to provide insights into a population mean.

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Cumulative Probability Distribution Functions (CDFs)

6K views · 1y ago · 19:32

Cumulative Probability Distribution Functions (CDFs) Learn how to work with cumulative probability distribution functions (CDFs) for both discrete and continuous random variables. In this video, we define CDFs, show how they accumulate probabilities, and compare their formulas

✦ Diagonalization / Diagonalizing a Matrix, Part 2 ✦

7K views · 2y ago · 13:30

Diagonalization Part 2 | Solving the Example of Matrix A In this follow-up video, we continue our journey into matrix diagonalization by working through the example introduced in the previous video. We'll apply the diagonalization process to matrix A and fully break down each step, from calculating eigenvalues and eigenvectors to constructing matrices P and D. This video will solidify your understanding of diagonalization by seeing it applied in practice.

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✦ Diagonalization / Diagonalizing a Matrix, Part 1 ✦

16K views · 2y ago · 7:25

In this introductory video, we cover the basics of matrix diagonalization, focusing on the core concept of representing a matrix A = PDP ^(−1). This powerful technique simplifies the computation of matrix powers, making it much easier to calculate A^k. You’ll see the step-by-step process, including finding eigenvalues and eigenvectors, constructing matrices P and D, and using them to diagonalize A.

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Ladder Networks, Circuits, Transfer Matrix, LU Factorizations

1K views · 2y ago · 15:52

Matrix LU Factorizations | Circuits and the Transfer Matrix In this video, we'll delve into the application of matrix and LU factorizations in the context of electrical circuits, focusing on transfer matrices in ladder networks. Using matrices to model circuits helps analyze and simplify complex networks. Here, you'll see how input and output voltages and currents relate through a transfer matrix, a valuable tool in electrical engineering.

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✦ LU Matrix Factorization, Example 2 ✦

1K views · 2y ago · 8:36

Learn how to perform LU Factorization of matrices step-by-step. This video covers transforming a matrix A into lower (L) and upper (U) triangular matrices, with detailed row operations to reach echelon form. Understand the benefits of LU Factorization in solving systems of equations and simplifying matrix operations. Perfect for students and anyone studying linear algebra or advanced mathematics.

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✦ LU Matrix Factorization ✦

11K views · 2y ago · 30:41

Matrix LU Factorizations - Step-by-Step Guide to LU Decomposition In this video, we dive into LU factorization, a powerful method to decompose a matrix into a lower triangular matrix (L) and an upper triangular matrix (U). LU decomposition simplifies matrix operations, making it easier to solve linear systems and perform matrix inversions. We’ll explore how to perform LU factorization on a matrix, understand its applications, and demonstrate with step-by-step examples.

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Marginal Probability Density Functions

4K views · 2y ago · 12:58

Marginal Probability Density Functions | Discrete Random Variables In this video, we'll explore the concept of marginal probability density functions specifically for discrete random variables. Understanding the marginal distributions of individual variables from a joint distribution is essential for analyzing probabilities independently. You'll learn how to calculate the marginal probability of X and Y for discrete random variables.

Determinants of Triangular Matrices

3K views · 2y ago · 11:17

In this video, we dive into calculating the determinants of triangular matrices using an easy-to-follow, step-by-step approach. Triangular matrices offer a simpler path to determining matrix determinants, but understanding the process and rules is essential. We start with a matrix example, transforming it into a triangular form and then proceed to find its determinant by multiplying the diagonal entries.

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Joint Probability Density Functions and Bivariate Random Variables

6K views · 2y ago · 14:15

Understanding Joint Probability Density Functions | Examples and Key Concepts In this video, we examine joint probability density functions (PDFs), a key concept in probability and statistics that describes the likelihood of multiple random variables occurring together. Through clear explanations and examples, we'll explore how joint PDFs work, why they're important, and how they apply in real-world scenarios involving bivariate random variables.

Determinant of a Triangular Matrix

1K views · 2y ago · 12:29

Learn how to calculate the determinants of triangular matrices quickly and efficiently! In this video, we break down the process for finding the determinant of a triangular matrix (upper or lower) by focusing on key concepts and step-by-step explanations. If you’re studying linear algebra or preparing for exams, understanding this shortcut can save you a lot of time and effort.

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Points on Ellipse Farthest from a Given Point

1K views · 2y ago · 13:12

Optimization: Finding Points on an Ellipse Farthest from a Given Point In this video, we explore an optimization problem where we aim to find the point(s) an the ellipse defined furthest away from a specified point. We'll walk through the process step by step, including setting up the distance function and using calculus techniques to optimize the distance.

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Sketch the Derivative: Position, Velocity, and Acceleration

1K views · 2y ago · 8:14

Sketching the Derivative of a Function: Position, Velocity, and Acceleration In this video, we explore how to sketch the derivative of a function, using examples from physics like position, velocity, and acceleration. Given the graph of a position function s(t), we will find the corresponding velocity v(t) and acceleration a(t) graphs. By analyzing slopes and changes, we can better understand how derivatives reflect rates of change in real-world scenarios.

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Sketching the Derivative of a Function

4K views · 2y ago · 29:52

In this video we look at how to sketch the derivative graph of a given function. We look at many examples where we take the graph of f(x) and then sketch f '(x).

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Solving Quadratic Inequalities By Graphing and Algebra

2K views · 2y ago · 1:02:46

In this video, we will explore how to solve quadratic inequalities using two different methods: graphing and algebraic approaches. I demonstrate how to solve many quadratic inequalities. by analyzing the graph of the quadratic function and applying test points for accuracy. Then, we break down how to factor the quadratic expression and determine the solution intervals algebraically.

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Determinant of 4x4 Matrix

35K views · 2y ago · 9:00

How to Find the Determinant of a 4x4 Matrix Using Cofactors. In this video, I demonstrate how to find the determinant of a 4x4 matrix using the method of cofactors. You'll see a complete, step-by-step example that breaks down the process of expanding along a row or column to calculate the determinant of a larger matrix.

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❖ Horizontal and Vertical Shifts Using f(x) = x^4 - Fast Example! ❖

1K views · 2y ago · 2:16

Horizontal and Vertical Shifts Using f(x) = x^4 In this video, we'll explore how to perform both horizontal and vertical shifts on the parent function f(x) = x^4. This quick example demonstrates how shifting transformations work, moving through the process a bit faster for those who are looking for a quick refresher on graph transformations. Ideal for anyone familiar with basic graphing techniques who wants to brush up on shifting transformations.

❖ The Law Of Cosines SAS Example ❖

1K views · 2y ago · 5:06

The Law of Cosines: SAS Example Explained Unlock the Law of Cosines with a Quick SAS Example! In this video, we dive into the Law of Cosines using a straightforward example involving the Side-Angle-Side (SAS) scenario. Here, we know the lengths of two sides and the angle between them, and we’ll use this information to calculate the length of the missing side.

❖ The Law of Cosines - SSS Example ❖

1K views · 2y ago · 2:43

In this video we look at an example involving the Law of Cosines. In this triangle we are given the 3 sides of the triangle and asked to find the measure of the smallest angle. In order to solve the question we merely use the Law of Cosines. This is just a quick example to refresh or quiz yourself!

❖ 3x3 Determinant Shortcut: Find the Determinant of a 3x3 Matrix ❖

9K views · 2y ago · 4:44

Shortcut for Finding the Determinant of a 3x3 Matrix - Step-by-Step Guide In this video, I introduce a quick and efficient method to find the determinant of a 3x3 matrix. Follow along as I break down the steps for calculating determinants using a shortcut, making it easier to solve linear algebra problems quickly. You'll learn how to apply this technique to the matrix

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Hypothesis Test: Difference in Population Means, Standard Deviations Unknown

44K views · 2y ago · 14:41

Guest: Hypothesis Test

In this video we estimate the difference in population means between two populations of interest. In many examples, we will consider the difference of the two populations to be equal to zero, suggesting that there is no difference between two populations. In my complete hypothesis test example, we collect data to try and determine whether or not using a calculator on an exam gives any noticeable advantage on an exam.

❖ Full Hypothesis Test, Ex 2' ❖

2K views · 2y ago · 6:21

This example skips a lot of the details and shows how to quickly compute the solution.

Daily Math Puzzle #3 'How Many Squares and Rectangles are On a Chessboard?' #maths #puzzle

2K views · 2y ago · 9:06

Here we are asked how many squares cover a chessboard (1 x 1, 2 x 2, etc..) and also how many rectangles are on a chessboard. A solution is also provided to both questions.

Daily Math Puzzle #2 #maths #puzzle #games #problemsolving

1K views · 2y ago · 8:46

Question: There are two kinds of students in a class, those who lie and those who do not. Each student knows which kind of student the other is. In a meeting today, each student tells what kind of student the other student is. The answer 'liar' is given 240 times. Yesterday a similar meeting happened with one student missing. The answer liar was given 216 times. How many students are present today?

Daily Math Puzzle #1, Can You Solve It? #maths #puzzle #dailypuzzle #competitionmath

1K views · 2y ago · 5:35

This is video #1 of my 'Daily Math Puzzle' series. The questions are intended to be brain teasers or puzzles of varying difficulty for those interested in recreational math and puzzle solving. In this question, we have the digits one through five that must be arranged in a star pattern. We want to consider all such possible diagrams. We are interested in finding the probability of selecting a diagram at random so that at least one edge links consecutive numbers.

❖ Understanding Contingency Tables: Hypothesis Testing Explained with Real-Life Examples ❖

2K views · 2y ago · 21:18

Guest: Real-Life Examples

Understanding Contingency Tables: Hypothesis Testing Explained with Real-Life Examples In this informative video, we dive into contingency tables and their role in hypothesis testing! Discover how to determine if two categorical variables are independent by analyzing observed data and expected counts. This method closely relates to the chi-square test, making it an essential concept for statistics students and professionals alike.

❖ Solving a First Order Linear Differential Equation: (1 + x)y' - xy = x + x^2 ❖

1K views · 2y ago · 17:42

Solving a First Order Linear Differential Equation: Step-by-Step Guide In this video, we solve the first-order linear differential equation (1 + x)y' - xy = x + x2. To tackle this problem, we first perform some algebra to simplify the equation and then find the integrating factor. After multiplying both sides by the integrating factor, we solve the equation by using integration by parts multiple times.

Free Homework Help with PatrickJMT : Come ask a question and I will try to help!

2K views · 2y ago · 1:07:21

Just some free drop-in homework help! Arithmetic through college stuff. Here til I leave! :)

#HONORIFA2024: Check out HONOR's cool new product feature!

2K views · 2y ago · 4:44

❖ The Chi-Square Distribution in Statistics ❖

2K views · 2y ago · 22:09

In this video I give an overview of what the Chi-Square distribution is in Statistics. I discuss ok the general concept and give a few different examples to illustrate the idea. In the video I also discuss how to use a chi-square table, how to compute a test statistic, and other basic but useful info. In the next video I will perform a 'real life' example using a hypothesis test involving chi-square.