chapter one

.gitignore

@@ -0,0 +1 @@
+.env

README.md

@@ -4,3 +4,12 @@ My roadmap for becoming competent quant and capable of creating automated tradin
 
 Current Goal: **Learn Quantitative Foundations**
 
+## Other
+
+issue templating
+reading        # blue
+coding         # green
+exam           # orange
+writeup        # purple
+research       # yellow
+bug            # red  (for when your code breaks)

probability-statistics-random-processes/.ipynb_checkpoints/ch1-checkpoint.ipynb

@@ -0,0 +1,203 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "a6732353-51d5-4478-9cf8-5834e57e5a4e",
+   "metadata": {},
+   "source": [
+    "# Chapter 1 Notes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "48d9ec9e-83da-40ca-ae79-3c45f8af137c",
+   "metadata": {},
+   "source": [
+    "## Main Concepts\n",
+    "\n",
+    "Outcome: A result of a random experiment.\n",
+    "\n",
+    "Sample Space: The set of all possible outcomes.\n",
+    "\n",
+    "Event: A subset of the sample space.\n",
+    "\n",
+    "Inclusion-exclusion principle holds for probability\n",
+    "\n",
+    "Consider a sample space S. If S is a countable set, this refers to a discrete probability\n",
+    "mode\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ac122be-50b2-423c-b88f-e4b3327b21bd",
+   "metadata": {},
+   "source": [
+    "## Example Problems"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7fb87a35-a470-4d98-935f-80c814e3f95d",
+   "metadata": {},
+   "source": [
+    "Example 1.5 - soln\n",
+    "\n",
+    "- there are 10 people with white shirts and 8 people with red shirts;\n",
+    "- 4 people have black shoes and white shirts\n",
+    "- 3 people have black shoes and red shirts\n",
+    "- the total number of people with white or red shirts or black shoes is 21\n",
+    "\n",
+    "Let A be the set of people with white shirts, B be the set of people with red shirts and let C be the set of people with black shoes.\n",
+    "\n",
+    "\\begin{align*}\n",
+    "|A|=10 \\\\\n",
+    "|B|=8 \\\\\n",
+    "|A \\cap C| = 4 \\\\\n",
+    "|B \\cap C| = 3 \\\\\n",
+    "|A \\cup B \\cup C| = 21\n",
+    "\\end{align*}\n",
+    "\n",
+    "Now we solve for $|C|$:\n",
+    "\n",
+    "\\begin{align*}\n",
+    "|A| + |B| + |C| - |A \\cap B| - |A \\cap C| - |B \\cap C| + |A \\cap B \\cap C| = 21 \\\\\n",
+    "10 + 8 + |C| - 0 - 4 - 3 - 0 = 21 \\\\\n",
+    "18 + |C| - 7 = 21 \\\\\n",
+    "|C| + 11 = 21 \\\\\n",
+    "|C| = 10\n",
+    "\\end{align*}\n",
+    "\n",
+    "$\\therefore$ number of people with black shoes is 10\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "72b40733-531a-48f3-9879-75601684afc2",
+   "metadata": {},
+   "source": [
+    "Example 1.11 - soln\n",
+    "\n",
+    "Suppose we have the following information:\n",
+    "1. There is a 60 percent chance that it will rain today.\n",
+    "2. There is a 50 percent chance that it will rain tomorrow.\n",
+    "3. There is a 30 percent chance that it does not rain either day.\n",
+    "\n",
+    "T = rains\n",
+    "F = no rain\n",
+    "\n",
+    "$S = \\{(F, F), (F, T), (T, F), (T, T)\\}$\n",
+    "\n",
+    "$P((T, F) \\cup (T, T)) = 0.6$\n",
+    "\n",
+    "$P((F, T) \\cup (T, T)) = 0.5$\n",
+    "\n",
+    "$P((F, F)) = 0.3$\n",
+    "\n",
+    "\\begin{align*}\n",
+    "P(S) = 1 \\\\\n",
+    "P(\\{(F, F)\\} \\cup \\{(F, T)\\} \\cup \\{(T, F)\\} \\cup \\{(T, T)\\}) = 1 \\\\\n",
+    "P((F,F)) + P(\\{(F, T)\\} \\cup \\{(T, F)\\} \\cup \\{(T, T)\\}) = 1 \\\\\n",
+    "0.3 + P(\\{(F, T)\\} \\cup \\{(T, F)\\} \\cup \\{(T, T)\\}) = 1 \\\\\n",
+    "P(\\{(F, T)\\} \\cup \\{(T, F)\\} \\cup \\{(T, T)\\}) = 0.7 \\\\\n",
+    "P(\\{(F, T)\\} \\cup \\{(T, T)\\}) + P((T, F)) = 0.7 \\\\\n",
+    "0.5 + P((T, F)) = 0.7 \\\\\n",
+    "P((T, F)) = 0.2 \\\\\n",
+    "P(\\{(T, F)\\} \\cup \\{(T, T)\\}) + P((F, T)) = 0.7 \\\\\n",
+    "P((F, T)) = 0.1\n",
+    "\\end{align*}\n",
+    "\n",
+    "Find the following probabilities:\n",
+    "\n",
+    "a. The probability that it will rain today or tomorrow.\n",
+    "\n",
+    "\\begin{align*}\n",
+    "P((T, F) \\cup (F, T) \\cup (T, T)) = 0.7\n",
+    "\\end{align*}\n",
+    "\n",
+    "b. The probability that it will rain today and tomorrow.\n",
+    "\n",
+    "\\begin{align*}\n",
+    "P((T, T)) = 1 - 0.3 - 0.2 - 0.1 = 0.4\n",
+    "\\end{align*}\n",
+    "\n",
+    "c. The probability that it will rain today but not tomorrow.\n",
+    "\n",
+    "\\begin{align*}\n",
+    "P((T, F)) = 0.2\n",
+    "\\end{align*}\n",
+    "\n",
+    "d. The probability that it either will rain today or tomorrow, but not both.\n",
+    "\n",
+    "\\begin{align*} \n",
+    "P(\\{(T, F)\\} \\cup \\{(F, T)\\}) = P((T, F)) + P((F, T)) = 0.2 + 0.1 = 0.3\n",
+    "\\end{align*}\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8b5131dd-5ebd-4156-b808-f8df273317fb",
+   "metadata": {},
+   "source": [
+    "Example 1.12 - soln\n",
+    "\n",
+    "$S = \\{ -1, 0, 1, 2, 3, ... \\}$\n",
+    "\n",
+    "$\\forall x \\in S, P(x) = \\frac{1}{2^{x + 2}}$\n",
+    "\n",
+    "What is the probability that I win more than or equal to 1 dollar and less than 4 dollars?\n",
+    "\n",
+    "\\begin{align*} \n",
+    "P({1, 2, 3}) = P(1) + P(2) + P(3) \\\\\n",
+    "= 1/8 + 1/16 + 1/32\n",
+    "\\end{align*}\n",
+    "\n",
+    "What is the probability that I win more than 2 dollars?\n",
+    "\n",
+    "\\begin{align*} \n",
+    "\\sum_{i=3}^{\\infty} P(i) = P(3) + P(4) + P(5) + P(6) + ... \\\\\n",
+    "= 1/32 + 1/64 + 1/128 + 1/256 + ... \\\\\n",
+    "=\\frac{\\frac{1}{32}}{1 - \\frac{1}{2}}\n",
+    "=\\frac{1}{16}\n",
+    "\\end{align*}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "69962960-18a6-436b-b9eb-9a6dfae7559a",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11163495-a6cc-43b9-bf41-02748b13d210",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.14.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

probability-statistics-random-processes/.ipynb_checkpoints/notes-checkpoint.md

@@ -0,0 +1,3 @@
+# Notes for Introduction to Probability, Statistics, and Random Processes
+
+## Ch.1

probability-statistics-random-processes/ch1.ipynb

@@ -0,0 +1,244 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "a6732353-51d5-4478-9cf8-5834e57e5a4e",
+   "metadata": {},
+   "source": [
+    "# Chapter 1 Notes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "48d9ec9e-83da-40ca-ae79-3c45f8af137c",
+   "metadata": {},
+   "source": [
+    "## Main Concepts\n",
+    "\n",
+    "Outcome: A result of a random experiment.\n",
+    "\n",
+    "Sample Space: The set of all possible outcomes.\n",
+    "\n",
+    "Event: A subset of the sample space.\n",
+    "\n",
+    "Inclusion-exclusion principle holds for probability\n",
+    "\n",
+    "Consider a sample space S. If S is a countable set, this refers to a discrete probability\n",
+    "mode\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ac122be-50b2-423c-b88f-e4b3327b21bd",
+   "metadata": {},
+   "source": [
+    "## Example Problems"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7fb87a35-a470-4d98-935f-80c814e3f95d",
+   "metadata": {},
+   "source": [
+    "Example 1.5 - soln\n",
+    "\n",
+    "- there are 10 people with white shirts and 8 people with red shirts;\n",
+    "- 4 people have black shoes and white shirts\n",
+    "- 3 people have black shoes and red shirts\n",
+    "- the total number of people with white or red shirts or black shoes is 21\n",
+    "\n",
+    "Let A be the set of people with white shirts, B be the set of people with red shirts and let C be the set of people with black shoes.\n",
+    "\n",
+    "\\begin{align*}\n",
+    "|A|=10 \\\\\n",
+    "|B|=8 \\\\\n",
+    "|A \\cap C| = 4 \\\\\n",
+    "|B \\cap C| = 3 \\\\\n",
+    "|A \\cup B \\cup C| = 21\n",
+    "\\end{align*}\n",
+    "\n",
+    "Now we solve for $|C|$:\n",
+    "\n",
+    "\\begin{align*}\n",
+    "|A| + |B| + |C| - |A \\cap B| - |A \\cap C| - |B \\cap C| + |A \\cap B \\cap C| = 21 \\\\\n",
+    "10 + 8 + |C| - 0 - 4 - 3 - 0 = 21 \\\\\n",
+    "18 + |C| - 7 = 21 \\\\\n",
+    "|C| + 11 = 21 \\\\\n",
+    "|C| = 10\n",
+    "\\end{align*}\n",
+    "\n",
+    "$\\therefore$ number of people with black shoes is 10\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "72b40733-531a-48f3-9879-75601684afc2",
+   "metadata": {},
+   "source": [
+    "Example 1.11 - soln\n",
+    "\n",
+    "Suppose we have the following information:\n",
+    "1. There is a 60 percent chance that it will rain today.\n",
+    "2. There is a 50 percent chance that it will rain tomorrow.\n",
+    "3. There is a 30 percent chance that it does not rain either day.\n",
+    "\n",
+    "T = rains\n",
+    "F = no rain\n",
+    "\n",
+    "$S = \\{(F, F), (F, T), (T, F), (T, T)\\}$\n",
+    "\n",
+    "$P((T, F) \\cup (T, T)) = 0.6$\n",
+    "\n",
+    "$P((F, T) \\cup (T, T)) = 0.5$\n",
+    "\n",
+    "$P((F, F)) = 0.3$\n",
+    "\n",
+    "\\begin{align*}\n",
+    "P(S) = 1 \\\\\n",
+    "P(\\{(F, F)\\} \\cup \\{(F, T)\\} \\cup \\{(T, F)\\} \\cup \\{(T, T)\\}) = 1 \\\\\n",
+    "P((F,F)) + P(\\{(F, T)\\} \\cup \\{(T, F)\\} \\cup \\{(T, T)\\}) = 1 \\\\\n",
+    "0.3 + P(\\{(F, T)\\} \\cup \\{(T, F)\\} \\cup \\{(T, T)\\}) = 1 \\\\\n",
+    "P(\\{(F, T)\\} \\cup \\{(T, F)\\} \\cup \\{(T, T)\\}) = 0.7 \\\\\n",
+    "P(\\{(F, T)\\} \\cup \\{(T, T)\\}) + P((T, F)) = 0.7 \\\\\n",
+    "0.5 + P((T, F)) = 0.7 \\\\\n",
+    "P((T, F)) = 0.2 \\\\\n",
+    "P(\\{(T, F)\\} \\cup \\{(T, T)\\}) + P((F, T)) = 0.7 \\\\\n",
+    "P((F, T)) = 0.1\n",
+    "\\end{align*}\n",
+    "\n",
+    "Find the following probabilities:\n",
+    "\n",
+    "a. The probability that it will rain today or tomorrow.\n",
+    "\n",
+    "\\begin{align*}\n",
+    "P((T, F) \\cup (F, T) \\cup (T, T)) = 0.7\n",
+    "\\end{align*}\n",
+    "\n",
+    "b. The probability that it will rain today and tomorrow.\n",
+    "\n",
+    "\\begin{align*}\n",
+    "P((T, T)) = 1 - 0.3 - 0.2 - 0.1 = 0.4\n",
+    "\\end{align*}\n",
+    "\n",
+    "c. The probability that it will rain today but not tomorrow.\n",
+    "\n",
+    "\\begin{align*}\n",
+    "P((T, F)) = 0.2\n",
+    "\\end{align*}\n",
+    "\n",
+    "d. The probability that it either will rain today or tomorrow, but not both.\n",
+    "\n",
+    "\\begin{align*} \n",
+    "P(\\{(T, F)\\} \\cup \\{(F, T)\\}) = P((T, F)) + P((F, T)) = 0.2 + 0.1 = 0.3\n",
+    "\\end{align*}\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8b5131dd-5ebd-4156-b808-f8df273317fb",
+   "metadata": {},
+   "source": [
+    "Example 1.12 - soln\n",
+    "\n",
+    "$S = \\{ -1, 0, 1, 2, 3, ... \\}$\n",
+    "\n",
+    "$\\forall x \\in S, P(x) = \\frac{1}{2^{x + 2}}$\n",
+    "\n",
+    "What is the probability that I win more than or equal to 1 dollar and less than 4 dollars?\n",
+    "\n",
+    "\\begin{align*} \n",
+    "P({1, 2, 3}) = P(1) + P(2) + P(3) \\\\\n",
+    "= 1/8 + 1/16 + 1/32\n",
+    "\\end{align*}\n",
+    "\n",
+    "What is the probability that I win more than 2 dollars?\n",
+    "\n",
+    "\\begin{align*} \n",
+    "\\sum_{i=3}^{\\infty} P(i) = P(3) + P(4) + P(5) + P(6) + ... \\\\\n",
+    "= 1/32 + 1/64 + 1/128 + 1/256 + ... \\\\\n",
+    "=\\frac{\\frac{1}{32}}{1 - \\frac{1}{2}}\n",
+    "=\\frac{1}{16}\n",
+    "\\end{align*}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4609aba5-dfdc-4500-bec2-cfa2e544cca7",
+   "metadata": {},
+   "source": [
+    "Example 1.17 - soln\n",
+    "\n",
+    "I roll a fair die twice and obtain two numbers X1 = result of the first roll and X2 = result\n",
+    "of the second roll. Given that I know X1 + X2 = 7, what is the probability that X1 = 4 or\n",
+    "X2 = 4?\n",
+    "\n",
+    "What is our sample space?\n",
+    "\\begin{align*} \n",
+    "D = \\{1,2,3,4,5,6\\} \\\\\n",
+    "S = D \\times D\n",
+    "\\end{align*}\n",
+    "\n",
+    "\\begin{align*} \n",
+    "P(A|B) = \\frac{P(A \\cap B)}{P(B)}\n",
+    "\\end{align*}\n",
+    "\n",
+    "\\begin{align*} \n",
+    "A = \\{(x,y) \\mid x=4 \\lor y = 4 \\} \\\\\n",
+    "|A| = 12 \\\\\n",
+    "P(A) = \\frac{|A|}{|S|} \\\\\n",
+    "= \\frac{12}{36} = \\frac{1}{3}\n",
+    "\\end{align*}\n",
+    "\n",
+    "\\begin{align*} \n",
+    "B = \\{(x,y) \\mid x+y = 7 , x,y \\in \\mathbb{N}\\} \\\\\n",
+    "|B| = 6 \\\\\n",
+    "P(B) = \\frac{1}{6} \\\\\n",
+    "\\end{align*}\n",
+    "\n",
+    "\\begin{align*} \n",
+    "P(A \\cap B) = \\frac{1}{18}\n",
+    "\\end{align*}\n",
+    "\n",
+    "\n",
+    "\\begin{align*} \n",
+    "B = \\{(x,y) \\mid x+y = 7 , x,y \\in \\mathbb{N}\\} \\\\\n",
+    "A = \\{(x,y) \\mid x=4 \\lor y = 4 \\} \\\\\n",
+    "P(A|B) = \\frac{P(A \\cap B)}{P(B)} \\\\\n",
+    "= \\frac{P(A \\cap B)}{P(B)} \\\\\n",
+    "= \\frac{\\frac{1}{18}}{\\frac{1}{6}}\n",
+    "= \\frac{6}{18} = \\frac{1}{3}\n",
+    "\\end{align*}\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11163495-a6cc-43b9-bf41-02748b13d210",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.14.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

probability-statistics-random-processes/notes.md

@@ -0,0 +1,3 @@
+# Notes for Introduction to Probability, Statistics, and Random Processes
+
+## Ch.1

scripts/create-issues-batch.py

@@ -0,0 +1,63 @@
+import json
+import urllib.request
+
+# --- MANDATORY AUTH CONFIGURATION ---
+GITEA_URL = "http://git.burke.lan:3000"  # No trailing slash
+TOKEN = ""
+OWNER = "burkkyy"
+REPO = "roadmap"
+MILESTONE_ID = 1  
+
+TASKS = [
+    # {"title": "", "body": ""},
+]
+
+CHAPTERS = [
+    "Ch.3",
+    "Ch.4",
+    "Ch.5",
+    "Ch.6",
+    "Ch.7",
+    "Ch.8",
+    "Ch.9",
+    "Ch.10",
+    "Ch.12",
+    "Ch.13",
+    "Ch.14",
+]
+
+for ch in CHAPTERS:
+    TASKS.append({"title": f"{ch} - Problems", "body": f""})
+
+
+headers = {
+    "Authorization": f"token {TOKEN}",
+    "Content-Type": "application/json",
+    "Accept": "application/json"
+}
+
+url = f"{GITEA_URL}/api/v1/repos/{OWNER}/{REPO}/issues"
+
+if not TASKS:
+    print("Warning: 'TASKS' list is empty. Please populate your task templates before running.")
+    exit(1)
+
+for task in TASKS:
+    title = task["title"]
+    body = task["body"]
+    
+    payload = {
+        "title": title,
+        "body": body,
+        "milestone": int(MILESTONE_ID)
+    }
+    
+    data = json.dumps(payload).encode('utf-8')
+    req = urllib.request.Request(url, data=data, headers=headers, method="POST")
+    
+    try:
+        with urllib.request.urlopen(req) as response:
+            if response.status == 201:
+                print(f"Successfully created issue: {title}")
+    except Exception as e:
+        print(f"Failed to create issue '{title}': {e}")