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Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past or is happening now outside our immediate experience. Uncertainty has been called the ...

Probability Distribution Notes: Probability is a fundamental aspect of mathematics that helps us understand and quantify uncertainty. Mastery of this subject is essential for students, as it has ...

In A Philosophical Essay on Probabilities, published in 1814, Pierre-Simon Laplace introduced a notorious hypothetical creature: a “vast intelligence” that knew the complete physical state of the ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

Worse, the models “hallucinate” — meaning, they invent. A study of AI tools used in the legal domain shows 58% to 82% ...

After you read this, you’ll have a 32% chance at better understanding how bad you are at probability. If the risk of an event goes up or down, we assume that it will keep changing in that direction.

This important study reports three experiments examining how the subjective experience of task regularities influences perceptual decision-making. Although the evidence linking subjective ratings to ...

The probability that a tennis player wins the first set of a match is \(\frac{3}{5}\). If she wins the first set, the probability that she wins the second set is \(\frac{9}{10}\). If she loses the ...