Category Archives: probability

Central Limit Theorem, Normal Distribution and Entropy

A simple form of The Central Limit Theorem: For identically independent distributed random vectors ; let . If , . When I first learn the central limit theorem, I’m always curious why the sum of a large number of random … Continue reading

Posted in asymptotic, entropy, probability | 3 Comments

Convergence in Probability and Convergence with Probability 1

Definations: For a random vector and a sequence of random vectors defined on a probability space . 1. Convergence in Probability or Convergence of probability measures, is kind of convergence in measure, in concept of the measure theory. : for … Continue reading

Posted in analysis, convergence, probability | 24 Comments

Why the point probability of a continuous distribution is 0?

We all know that if a random variable is continuous distributed, the point probability of is 0. For example, , where means a uniform distribution with support in . Then for any . However, it is not that easy to understand why . The  confusion always comes from … Continue reading

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