From d176120b7e386bd934d82be2bd37942ab7c553fd Mon Sep 17 00:00:00 2001 From: Caleb Burke Date: Tue, 19 May 2026 23:33:50 -0700 Subject: [PATCH] chapter one --- .gitignore | 1 + README.md | 9 + .../.ipynb_checkpoints/ch1-checkpoint.ipynb | 203 +++++++++++++++ .../.ipynb_checkpoints/notes-checkpoint.md | 3 + .../ch1.ipynb | 244 ++++++++++++++++++ .../notes.md | 3 + scripts/create-issues-batch.py | 63 +++++ ...ocesses - Hossein Pishro-Nik_SOLUTIONS.pdf | Bin 0 -> 4418925 bytes 8 files changed, 526 insertions(+) create mode 100644 .gitignore create mode 100644 probability-statistics-random-processes/.ipynb_checkpoints/ch1-checkpoint.ipynb create mode 100644 probability-statistics-random-processes/.ipynb_checkpoints/notes-checkpoint.md create mode 100644 probability-statistics-random-processes/ch1.ipynb create mode 100644 probability-statistics-random-processes/notes.md create mode 100644 scripts/create-issues-batch.py create mode 100644 textbooks/Introduction to Probability, Statistics, and Random Processes - Hossein Pishro-Nik_SOLUTIONS.pdf diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..4c49bd7 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +.env diff --git a/README.md b/README.md index b944c4f..0efd606 100644 --- a/README.md +++ b/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) diff --git a/probability-statistics-random-processes/.ipynb_checkpoints/ch1-checkpoint.ipynb b/probability-statistics-random-processes/.ipynb_checkpoints/ch1-checkpoint.ipynb new file mode 100644 index 0000000..fbdf016 --- /dev/null +++ b/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 +} diff --git a/probability-statistics-random-processes/.ipynb_checkpoints/notes-checkpoint.md b/probability-statistics-random-processes/.ipynb_checkpoints/notes-checkpoint.md new file mode 100644 index 0000000..bae2d32 --- /dev/null +++ b/probability-statistics-random-processes/.ipynb_checkpoints/notes-checkpoint.md @@ -0,0 +1,3 @@ +# Notes for Introduction to Probability, Statistics, and Random Processes + +## Ch.1 diff --git a/probability-statistics-random-processes/ch1.ipynb b/probability-statistics-random-processes/ch1.ipynb new file mode 100644 index 0000000..dbc4954 --- /dev/null +++ b/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 +} diff --git a/probability-statistics-random-processes/notes.md b/probability-statistics-random-processes/notes.md new file mode 100644 index 0000000..bae2d32 --- /dev/null +++ b/probability-statistics-random-processes/notes.md @@ -0,0 +1,3 @@ +# Notes for Introduction to Probability, Statistics, and Random Processes + +## Ch.1 diff --git a/scripts/create-issues-batch.py b/scripts/create-issues-batch.py new file mode 100644 index 0000000..3d3beb9 --- /dev/null +++ b/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}") \ No newline at end of file diff --git a/textbooks/Introduction to Probability, Statistics, and Random Processes - Hossein Pishro-Nik_SOLUTIONS.pdf b/textbooks/Introduction to Probability, Statistics, and Random Processes - Hossein Pishro-Nik_SOLUTIONS.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8908fd73ebd2359985582912adfa7d4421694758 GIT binary patch literal 4418925 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