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In this lecture, we look at an application of calculus to statistics. We have already de ned the probability density function f called PDF and its anti-derivative, the cumulative distribution
Probabilit´es”—“The Calculus of Probabilities.” The name has fallen out of fashion, perhaps due to the potential confusion with integral and differential calculus, but it seems particularly apt for our present topic. It suggests a system of rules that are generally useful for calculation, where the more modern “probability
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The goal is for you to understand how Statisticians came up with given formulas, i.e., which logical principles they were following. We will use various examples of traditional problems to illustrate concepts, but also more modern problems, e.g., problems from machine learning (computer vision, self-driving cars) that convey general applicability.
What is Calculus Based Statistics? Calculus Based statistics takes the four core concepts of calculus (Continuity, Limits, Definite integral, Derivative) and applies them to statistical theory. Essentially, non-calculus based statistics is for consumers of statistics and calculus based statistics is more suited for people who want to create ...
Statistics is the science of obtaining information from data. Because data are frequently modeled as arising from a random process, probability is central to the mathematical theory of statistics. This course will provide an introduction to both probability and statistics, focusing on applications.
Probability calculus and statistics. 1 The meaning of a probability. probability can be interpreted in different ways. In this book, we understand a probability to be an expression of how likely it is that an event will occur. Let us look at an example.
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Because data are frequently modeled as arising from a random process, probability is central to the mathematical theory of statistics. This course will provide an introduction to both probability and statistics, focusing on applications. We will cover most of chapters 1-25 of the textbook.