From 3ca496fdfaccfb3efa1a9df1a0a53995639a8930 Mon Sep 17 00:00:00 2001
From: Caleb Burke <calebburke91@gmail.com>
Date: Mon, 8 Jun 2026 01:46:12 -0700
Subject: [PATCH] more improved notes

---
 .../ch1/end-of-chapter-problems.ipynb         | 25 ----------
 .../ch2/notes.ipynb                           | 50 +++++++++++++++++++
 2 files changed, 50 insertions(+), 25 deletions(-)
 delete mode 100644 reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/end-of-chapter-problems.ipynb

diff --git a/reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/end-of-chapter-problems.ipynb b/reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/end-of-chapter-problems.ipynb
deleted file mode 100644
index 5ffd73b..0000000
--- a/reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/end-of-chapter-problems.ipynb	
+++ /dev/null
@@ -1,25 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "43cc5069",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d706c044",
-   "metadata": {},
-   "source": []
-  }
- ],
- "metadata": {
-  "language_info": {
-   "name": "python"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/reading/000_Introduction to Probability, Statistics, and Random Processes/ch2/notes.ipynb b/reading/000_Introduction to Probability, Statistics, and Random Processes/ch2/notes.ipynb
index a7a96c8..fecba61 100644
--- a/reading/000_Introduction to Probability, Statistics, and Random Processes/ch2/notes.ipynb	
+++ b/reading/000_Introduction to Probability, Statistics, and Random Processes/ch2/notes.ipynb	
@@ -63,6 +63,56 @@
     "\n",
     "- **unordered sampling with replacement:** $\\binom{n + k - 1}{k}$"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e93e0fe",
+   "metadata": {},
+   "source": [
+    "## Problem Solving Principles"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87279e59",
+   "metadata": {},
+   "source": [
+    "When solving a combinatorics problem, consider:\n",
+    "1. Does order matter?\n",
+    "    - Yes → Permutations\n",
+    "    - No → Combinations\n",
+    "\n",
+    "    - \"Are HHHTT and THHHT the same outcome to me?\"\n",
+    "\n",
+    "2. Are we sampling with of without replacement?\n",
+    "    - Without replacement → Hypergeometric (phone problem)\n",
+    "    - With replacement → Binomial (coin flips)\n",
+    "    \n",
+    "    \"Can the same item be chosen twice?\"\n",
+    "3. Are the \"groups\" labeled or unlabeled?\n",
+    "    - Labeled/distinguishable → Just multiply combinations\n",
+    "    - Unlabeled/interchangeable → Divide by k!\n",
+    "\n",
+    "    \"Does it matter which group is called group 1?\"\n",
+    "4. Are the items distinguishable?\n",
+    "    - Distinguishable → Each item is unique, classical probability applies\n",
+    "    - Indistinguishable → Outcomes are not equally likely, be careful\n",
+    "\n",
+    "      \"Could I label these items 1 to n?\"\n",
+    "5. Is complement of inclusion-exclusion easier?\n",
+    "    - Complement → When \"at least\" or \"at most\" language appears\n",
+    "    - Inclusion-Exclusion → When events overlap\n",
+    "\n",
+    "    \"Is the opposite event simpler to count?\"\n",
+    "6. Am I counting each outcome exactly once? \n",
+    "  - If yes, done. Otherwhise we are overcounting or undercounting"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9c5783dc",
+   "metadata": {},
+   "source": []
   }
  ],
  "metadata": {