Probability

CC BY-SA 4.0/Public domain/Public domain/Image by Author/Public domainOn Laplace’s brilliant solution to inverse probability and his discovery of the Central Limit TheoremIn the late 1600s, Jacob Bernoulli pondered over an interesting question: How do you estimate the probability of an event whose sample space is not fully accessible? How, for instance, do you estimate the chance of being hit in the head by a bolt from the sky during your lifetime? Or if you prefer a less dramatic setting, how do estimate the real…

Credit: Pixabay/CC0 Public Domain What happened to the scorching El Niño summer we were bracing for? Why has the east coast of Australia been drenched while the north and west gets the heat? For beachgoers, a wrong weather forecast is annoying. For farmers, it can be very expensive. And for northern Queensland residents surprised by flooding after…

Learn how to use simulations, replications, and for loops in R to answer many probability questionsContinue reading on Towards Data Science » Learn how to use simulations, replications, and for loops in R to answer many probability questionsContinue reading on Towards Data Science » FOLLOW US ON GOOGLE NEWS Read original article here Denial of responsibility! Techno Blender is an automatic aggregator of the all world’s media. In each content, the hyperlink to the primary source is specified. All trademarks…

Last updated: November 17th, 2023 at 15:37 UTC+01:00 Google is testing a new Memory Saver feature that will hopefully free up even more memory for Chrome users on desktop. The new feature, labeled “Probabilistic Memory Saver Mode,” uses probability distributions to estimate which tabs to keep or discard. Google first introduced the Chrome Memory Saver feature in December 2022. The mode frees up memory from inactive tabs to provide a smoother browsing experience for the active ones and lower overall Chrome memory…

Here’s a thought challenge for you: Let’s say I have chosen a particular second in time from the past nine years. Between November of 2014 and today, I am thinking of a specific (and totally random) year, month, day, hour, minute and second. Could you guess it? No chance? You have a better chance of guessing a specific second from a nine-year span than you have of winning the Powerball. Last month’s Powerball made headlines for topping a colossal $1.7 billion jackpot, the second largest in the game’s history (the winner…

Master the random variables and probability distributions and crack your next Data Science Interview with the third part of our Statistics Cheat Sheet seriesPhoto by Naser Tamimi on UnsplashIn mathematical terms, a random variable is a number whose value is dependent upon the outcome of a random event. For example, if we define the random variable (X) to be the number of times, we get a head while tossing a coin twice.Note: We use uppercase to denote the variable and lowercase to denote a single value of X. Here, x = 1…

take four arbitrary points on a sphere as the vertices of a tetrahedron. What is the probability that the centre of the sphere will be located within the tetrahedron?Reference: https://www.physicsforums.com/threads/probability-4-arbitrary-points-on-a-sphere.934671/ Consider four arbitrary points on a sphere, as the vertices of a tetrahedron. What is the probability that the centre of the sphere will be located within the tetrahedron?Puzzle – 4 points in a sphereSolution:Let’s first look into the problem in 2D:Points…

Temperature distribution over South Korea during 2021 early October. Credit: POSTECH In October 2021, South Korea experienced a heatwave of an unprecedented magnitude. During the first half of the month, the average temperature was recorded at 19.9 °C, marking a 3.9 °C increase above normal. This event was unparalleled, anticipated to arise only once in thousands of years. …

Conformal multi-quantile regression with CatboostTexas. Image by Author.In a previous article, we explored the capabilities of Catboost’s multi-quantile loss function, which allows for the prediction of multiple quantiles using a single model. This approach elegantly overcomes one of the limitations of traditional quantile regression, which necessitates the development of a separate model for each quantile, or storing the entire training set in the model. However, there is another disadvantage to quantile regression,…

In their paper, posted online in late November 2022, a key part of the proof involves showing that, for the most part, it doesn’t make sense to talk about whether a single die is strong or weak. Buffett’s dice, none of which is the strongest of the pack, are not that unusual: If you pick a die at random, the Polymath project showed, it’s likely to beat about half of the other dice and lose to the other half. “Almost every die is pretty average,” Gowers said.The project diverged from the AIM team’s original model in one…