连续随机变量
Continuous random variables
AI总结：
本文是融入量子思想的概率学导论，先讲离散概率，再讲连续概率相关分布、中心极限定理等，最后介绍随机矩阵与自由性。
AI中文摘要：
本文是一份概率学导论，撰写时融入了量子相关思想，即半圆律优先。首先讨论离散概率，重点包括二项分布、超几何分布（含正、负超几何分布）、泊松分布及复合泊松分布。随后进入连续概率领域，讲解该理论的基础，以指数分布、半圆分布、贝塔分布作为起始示例。接着研究中心极限定理与正态变量，涵盖实正态变量和复正态变量，同时也涉及瑞利分布与超球分布。最后，探讨若干更专业的分布及更专业的技术，并以随机矩阵与自由性的导论作为结尾。
英文摘要：
This is an introduction to probability, written with a quantum idea in mind, namely that the semicircle law comes first. We first discuss discrete probability, notably with the binomial and hypergeometric laws, positive and negative, and the Poisson and compound Poisson laws. Then we get into the continuous case, with the basics of the theory explained, and with as starting examples the exponential, semicircle and beta distributions. Afterwards, we investigate the central limits and normal variables, both real and complex, and with a look at Rayleigh laws, and hyperspherical laws too. Finally, we discuss a number of more specialized distributions, and more specialized techniques too, and we end with an introduction to random matrices and freeness.
