Tag: Probability

During your study of statistics, have you encountered the concepts of convergence in probability and convergence in distribution? Have you ever pondered why these concepts were introduced in the first place? If you have, then this story aims to help you answer some of those questions. Convergence...

Probability distributions are an essential component of statistical analysis in many fields, including finance, economics, engineering, and social sciences. Probability distributions provide a mathematical representation of the likelihood of different outcomes in a given scenario. Understanding prob...

Gamblers and Astronomers — the two very distinct groups of people who were actually responsible for the origination of probability theory. The former wanted to better grasp the odds while the latter was trying to have accurate observations from their rudimentary tools. Certainly, gambling i...

In the next series of discussions, we will discuss the topic of data using probability distributions. At the end of these discussions, we will have a clearer picture of data + science = data science. In the next post and onward, I will write about 16 different probability distributions commonly u...

The beta distribution is a continuous probability distribution for data with discrete outcomes. I’ll use an example to help us understand it better. Let’s say our store manager at the local supermarket did a stock count of the remaining green and red apples in the basket before closing t...

How confident can we be in a machine learning model’s prediction? This question has been a prominent area of research over the last decade, and it has major implications in high-stakes machine learning applications such as finance and healthcare. While many classification models, particularly&...

Prerequisites Before we begin, make sure you have Python installed on your machine. You can download and install Python from python.org. Additionally, we will be using the following Python libraries: NumPy: for numerical computations and array manipulation. Matplotlib: for data vi...

Suppose you have a binary classifier and two observations; the model scores them as 0.6 and 0.99, respectively. Is there a higher chance that the sample with the 0.99 score belongs to the positive class? For some models, this is true, but for others it might not. This blo...

Picture this: it’s a few years back, and my friends and I are gearing up for a post-graduation adventure to Goa. Excitement was high, but so was the uncertainty about the weather. My friends were optimistic, envisioning clear skies and endless sunshine. Meanwhile, I had a nagging feeling that ...

There are three outcomes to a chess game, winning, losing or a draw. And if you and I were playing against each other, me winning the game means you lose the game, vice versa. Today’s puzzle asks us to find the value of 1000P, where P is the probability that neither Rachel nor Steven is the...

The first approach is to consider the 13 different outcomes of the cards. To start, we know that there are four suits of cards, hearts, diamonds, spades, and clubs. In each suit, there are 13 cards, ranging from 2 to A. Therefore, each card has 1/13 probability. Let’s say you get a card with a...

Aspiring data scientists entering the realm of interviews often find themselves navigating a landscape heavily influenced by probability theory. Probability is a fundamental branch of mathematics that forms the backbone of statistical reasoning and data analysis. Proficiency in probability concep...

In this section, we will cover basics of probability and Combinatorics. That basic concept will help us to dive into the world of statistics and machine learning. Probability: Probability is the likelihood of an event occurring. This event can be pretty much anything — getting heads, ...

Here are some books on probability theory that are accessible to readers without a strong mathematical background: 1. “The Drunkard’s Walk: How Randomness Rules Our Lives” by Leonard Mlodinow — This book explores the role of randomness and probability in everyday...

In this section, we cover the basics of probability theory. We can calculate probabilities even if we only care a little about this section. So, you can skip this section if you already know the basics of probability. Firstly, we define Ω as an abstract set containing all possible outcomes of ...

Likelihood is a confusing term. Likelihood is not a probability, but is proportional to a probability; the two terms can’t be used interchangeably. In this post, we will be dissecting likelihood as a concept and understand it’s importance in machine learning. Intuition Let us under...

‌Joint Probability Joint probability is the likelihood of more than one event occurring at the same time P(A and B). The probability of event A and event B occurring together. It is the probability of the intersection of two or more events written as p(A ∩ B). ...

The banking industry has been applying machine learning to enhance loan approval process, default risk assessments, and fraud detection, for example. Making accurate decisions in these areas is important for effective risk management and cost control, which can translate to significant value. Whi...

I was in my high school statistics class. My eyes glazed over. The teacher talked about normal distributions and standard deviations. It wasn’t until I stumbled upon an illustrated book in the library that I saw these concepts in a new light. The book used graphics to show probability distribu...

Probability theory, a fundamental branch of mathematics, has long played a central role across various scientific disciplines. From the principles of uncertainty in physics to risk assessment in economics, and algorithm design in artificial intelligence, the influence of probability theory is omnipr...

In the world of mathematics, you’d expect that the chances of a child correctly matching their shoes to the right feet, or the possibility of correctly inserting a USB into a computer port, would stand at a clean 50 percent. This is based on the simple premise that there are two possible outco...

Random Variable: All possible outcomes of a random experiment are random variables. A random variable set is denoted by X. Discrete Distributions Bernoulli Distribution We have a single trial (only one observation) and 2 possible outcomes. For example, flipping a coin. Let’s...

Probability distributions are an essential component of statistical analysis in many fields, including finance, economics, engineering, and social sciences. Probability distributions provide a mathematical representation of the likelihood of different outcomes in a given scenario. Understanding prob...

Suppose you have a binary classifier and two observations; the model scores them as 0.6 and 0.99, respectively. Is there a higher chance that the sample with the 0.99 score belongs to the positive class? For some models, this is true, but for others it might not. This blo...

The beta distribution is a continuous probability distribution for data with discrete outcomes. I’ll use an example to help us understand it better. Let’s say our store manager at the local supermarket did a stock count of the remaining green and red apples in the basket before closing t...