Initial commit

Author: plalan-mw

README.md

@@ -0,0 +1,73 @@
+# Fundamentals of Probability Theory [![View <File Exchange Title> on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/####-NAME)
+**Curriculum Module**  
+_Created with R2021a. Compatible with R2021a and later releases._  
+
+## Description ##
+This package contains _[live scripts](https://www.mathworks.com/products/matlab/live-editor.html)_ and supporting files to teach the fundamental concepts in probability theory and statistical inference. These materials are designed to be flexible and can be easily modified to accommodate a variety of teaching and learning methods. Used in a sequence, the live scripts progressively add depth to the topic. However, each script or section can be easily adapted for standalone use. The live scripts include a brief background, interactive illustrations, tasks, reflection questions, and application examples. 
+
+This module can be used as part of a lecture, as activities in an instructional setting, or as interactive assignments to be completed outside of class. The live script sections contains direct instructions or tasks to illustrate the basics and additional reflection questions that are more open-ended.
+
+Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the **Stop** button in the **Run** section of the **Live Editor** tab in the MATLAB toolstrip.
+
+## Prerequisite Domain Knowledge ##
+This module assumes a knowledge of basic concepts in set theory, such as ⋃ (union) and ⋂ (intersection). It also assumes basic fluency in mathematical notation for Σ (summation) and Π (product). Other notation relevant to probability theory is introduced within the module as needed.
+
+## Suggested Prework ## 
+[MATLAB Onramp](https://www.mathworks.com/learn/tutorials/matlab-onramp.html) – a free two-hour introductory tutorial to learn the essentials of MATLAB®.  
+
+
+## Details ##  
+
+**`probabilityIntro.mlx`**   
+**Learning Goals**  
+- Explain the commonly used terms in probability such as random experiment, random process, trial, event, outcome, countable, equally likely, sample space, mutual independence.  
+- Define and compute classical probability of events.  
+    <img height="230" width="550" alt="classical probability" src="https://user-images.githubusercontent.com/81376570/134550273-b246a33e-87f7-4321-aa57-fe43f1fcba6a.png">   
+- Define and compute empirical probability of events.  
+    <img height="230" alt="empirical probability" src="https://user-images.githubusercontent.com/81376570/134533144-0c177d81-cea4-4232-95dd-fc0e9cb63800.gif">  
+- Explain the limitations and strengths of the subjective, classical, and empirical perspectives of probability.  
+- State and apply Kolmogorov's axioms of probability.   
+
+## ##
+
+**`randomVariables.mlx`, `randomVariableApp.mlapp`**  
+**Learning Goals**  
+- Define and create random variables to describe random processes.  
+- Generate an empirical distribution of random variables through random sampling.  
+- Explain the meaning of expectation and variance for random variables.  
+- Explain the difference between continuous and discrete random variables.  
+- Identify and use the discrete uniform and continuous normal probability distributions.  
+- Define and apply the probability density function and cumulative density function to find the probability of a random variable's value falling within a given interval.   
+- State the Central Limit Theorem and explain its implications for statistical inference.  
+
+
+<img height="400" alt="central limit theorem" src="https://user-images.githubusercontent.com/81376570/134528844-44efc801-83b8-446e-ba9d-5091fbf411ab.gif">    
+
+## ##
+**`inferenceBayes.mlx`**   
+**Learning Goals**  
+- Define conditional probability, and explain how it affects the sample space.   
+    <img height="600" alt="conditional probability" src="https://user-images.githubusercontent.com/81376570/134539490-24e6a992-f46c-4f78-b0e3-ac867d5304f8.png">   
+- State Bayes' theorem mathematically, and explain its implications for statistical inference.   
+    <img height="500" alt="conditional probability" src="https://user-images.githubusercontent.com/81376570/135294592-d9c61718-63c7-4197-81d2-0c4bb43c01b6.png">   
+- Apply Bayes' theorem to practical real-world problems.  
+
+**Data files:** `people.png`(optional)  
+
+
+## Products ##
+MATLAB, Statistics and Machine Learning Toolbox&trade;, Image Processing Toolbox&trade;
+
+## License ##
+The license for this module is available in the LICENSE.TXT file in this GitHub repository.
+
+## Educator Resources ##  
+- [Featured Courseware](https://www.mathworks.com/academia/courseware/course-materials.html)  
+- [Teach with MATLAB and Simulink ](https://www.mathworks.com/academia/educators.html) 
+- [MATLAB Grader](https://www.mathworks.com/products/matlab-grader.html)
+
+Have any questions or feedback? Contact the [MathWorks online teaching team](mailto:[email protected]).
+
+## ##
+
+_Copyright 2021 The MathWorks, Inc._

SECURITY.md

@@ -0,0 +1,6 @@
+# Reporting Security Vulnerabilities 
+
+If you believe you have discovered a security vulnerability, please report it to 
+[[email protected]](mailto:[email protected]). Please see 
+[MathWorks Vulnerability Disclosure Policy for Security Researchers](https://www.mathworks.com/company/aboutus/policies_statements/vulnerability-disclosure-policy.html) 
+for additional information.  

inferenceBayes.mlx

@@ -0,0 +1,11 @@
+Copyright (c) 2021, The MathWorks, Inc.
+All rights reserved.
+Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
+3. In all cases, the software is, and all modifications and derivatives of the software shall be, licensed to you solely for use in conjunction with MathWorks products and service offerings. 
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+
+