histogram
A histogram is a graph that shows how data are distributed by grouping values into bins (intervals) and showing how many observations fall into each bin. It’s perfect for visualizing: Think of it as stacking…
probability density
A probability density function describes the distribution of a continuous random variable. If is continuous, its PDF is a function such that: The key idea For continuous variables: The PDF is not a probability. Probability…
probability mass function
A probability mass function is a function that gives the probability of each individual value of a discrete random variable. If is a discrete random variable, then its PMF is: It tells you: A PMF…
Types of random variables
Most random variables fall into two big categories: Everything else is a refinement of these two. 🎯 1. Discrete Random Variables A discrete random variable takes countable values — usually integers. Key features Examples Common…
independent vs mutually exclusive
Independent vs. Mutually Exclusive 🎯 Mutually Exclusive (Disjoint) Events Two events are mutually exclusive if they cannot happen at the same time. Example:Rolling a die: 🎯 Independent Events Two events are independent if knowing one…
general addition rule
⭐ General Addition Rule The general addition rule tells you how to find the probability that A or B happens — even when the events overlap. 📌 The formula Why subtract the intersection?Because if A…
Independent event
⭐ Independent Events Two events are independent when one happening does not change the probability of the other. That’s the whole heart of it. 📌 Formal definition Events and are independent if This equation is…
Complementary events
⭐ Complementary Events Two events are complements when they cover the entire sample space together and cannot happen at the same time. If is an event, then its complement is: 📌 Key properties 🎯 Examples…
Sample and Event
⭐ Sample vs. Event Think of probability as a story with two levels: 🎯 Sample Space (S) The sample space is the complete list of everything that could happen in an experiment. Examples Key idea…
OpenAI’s Prism useful keyboard shortcuts and cool features
Prism (at https://prism.openai.com/) is OpenAI’s AI-powered collaborative LaTeX editor designed for researchers, scientists, and academics. It integrates frontier models (like GPT variants) directly into the LaTeX writing workflow for drafting, editing, rewriting, fixing errors, improving…
Downsampling Techniques for Custom Batches in training Machine Learning Models
Downsampling techniques can be used to create custom batches for training a machine learning model. These custom batches can be tailored to specific needs, such as improving training efficiency, handling imbalanced data, or focusing on…
downsampling for hyperparameter tuning
Downsampling for hyperparameter tuning reduces the dataset size to speed up model training and experimentation while preserving key data characteristics. Here’s a concise overview: Why Downsample for Hyperparameter Tuning? Key Considerations Practical Steps Pitfalls to…
OpenAI Prism: An excellent Free alternative to Overleaf for Scientific Writing and Collaboration?
If you work in research or academia, you know the struggle: you have your LaTeX editor open in one window, a dozen PDF tabs in another, and ChatGPT in a third. You’re constantly copying and…
Learn A1 Norwegian in the song “Min Familie”
Level: A1 (Beginner) Topic: Family, Introductions, and Descriptions Goal: Learn how to introduce family members and describe what they look like or do. Part 1: Vocabulary – Family Members (Familiemedlemmer) Let’s start by mapping out…
Learn A1-A2 Norwegian in the song “Min Hverdag”
Level: A1-A2 (Beginner) Topic: Daily Routine, Days of the Week, and Word Order Goal: Learn to describe your day and understand why the verb moves position in Norwegian sentences. Part 1: Vocabulary – Ukedagene (The…
Learn Norwegian A2-B1 in song: Livets Rytme (The Rhythm of Life)
level: A2-B1 1. Key Vocabulary Breakdown Let’s start by identifying the most useful nouns and verbs from the lyrics that you can use in daily conversation. Nouns (Substantiv): Verbs (Verbe): 2. Grammar Focus: The Imperative…
Norwegian B1-B2 in a ballad: Tidens Takt (The Pace of Time)
This lesson focuses on philosophical vocabulary, poetic word order, and essential verbs found in the lyrics. The song explores themes of time, responsibility, and human connection, making it excellent for intermediate learners (B1/B2 level) looking…
Fixed: No module named ‘frontend’ when importing fitz (PyMuPDF)
Error displayed: This error usually happens when PyMuPDF is not installed correctly or there’s a conflict with an outdated version. The fitz module should import directly from PyMuPDF, but if you see from frontend import…
Horizontal vs. Vertical App/Scenes in App
In most cases, horizontal apps have less ad inventory than vertical apps because their user base is broad but shallow, while vertical apps serve a narrower audience with deeper engagement, creating more targeted and monetizable…
How to reduce catastrophic forgetting when fine-tuning neural networks
Catastrophic forgetting occurs when a neural network “overwrites” what it learned in a previous task while training on a new one. This happens because the weights optimized for the first task are changed to minimize…
Textbooks Are All You Need
The central idea of the paper “Textbooks Are All You Need” is that data quality is significantly more important than data quantity or model size when training large language models (LLMs), particularly for code generation.…
Garlic and Onion Family: A Powerful Ally Against Cancer
Current research suggests that vegetables in the garlic family (Alliums) play a significant role in preventing cancer, particularly within the digestive system. Studies indicate that these vegetables can help combat cancers of the oesophagus, stomach,…
The “Speed” Myth of sloths
Baby sloths are born with their eyes open, all their teeth, and the ability to climb immediately.
Sloth’s Extreme Digestion & Bathroom Habits
Extreme Digestion & Bathroom Habits A Walking Ecosystem
openAi vs. ElevenLabs for natural text to speech: comparison + code
Both are excellent choices for “human-level” TTS, but they serve different needs. OpenAI is the budget-friendly, high-speed workhorse, while ElevenLabs is the premium “creative studio” for maximum realism and voice cloning. The Breakdown Feature OpenAI…