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Brownian motion:
The development of stochastic processes can be understood as a progressive refinement from simple discrete models to fully continuous ones. The first model in this refinement is the random walk, where time is discrete and the state evolves by fixed increments.…
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Probability theory and measure theory
The Axiomatic Foundation of Probability Theory Probability has been interpreted in several ways throughout its…
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Process counter simulator
A counting process on a time interval T=[0,1] can be simulated by assuming that events (or “arrivals”)…
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Analogy Between the Bernoulli Process (LLN) and the Server Security Model
This work examines the analogies between two stochastic simulations developed across the two assignments:the Bernoulli process…
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Server security
We are talking about server security over a period of n weeks. In this assignment…
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Recursive Statistics: Derivation and Online Implementation for Mean and Variance.
Recursive Arithmetic Mean The goal is to express the mean at step n, x̄n, in terms of the previous mean x̄n−1 and the new data point xn. Simplest Proof Derivation The definition of the arithmetic mean for n points is: Separate the sum into the sum of…
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Various averages:
We already know that location is where the distribution is located. Measures of Location: Where…
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Encryption with RSA
We’re going to talk about RSA. What is RSA? RSA is an asymmetrical algorithm created…
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LLN simulation:
The Law of Large Numbers (LLN) is a fundamental concept in probability theory. It states…
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Dataset and distribution:
The concept of a dataset is common to almost every scientific discipline where data provide the empirical…