Probability & Statistics Notes - Chapter 0

Chap 0 Introduction

0. 概述 INTRODUCTION

• 抽样调查 Questionnaire

  • Questions to gauge prior knowledge and experience with probability and statistics.

• 概率论是研究什么的? (What is Probability Theory?)

  • 研究和揭示随机现象的统计规律性的数学学科 (It is a mathematical discipline that studies and reveals the statistical laws of random phenomena).

• 自然界的现象 (Phenomena in Nature)

  • 确定现象 (Deterministic phenomenon): 在一定条件下必然发生的现象 (A phenomenon that inevitably occurs under certain conditions).
    • Examples:
      • 向空中抛一物体必然落向地面 (Free fall occurs whenever an object is acted upon by gravity alone).
      • 太阳早晨升起，傍晚下落 (The sun rises every morning and sets every evening).
      • 异性电荷相吸引 (Mutual attraction of anisotropic charges).
  • 随机现象 (Random phenomenon): 在试验或观察前无法预知出现什么结果 (A phenomenon whose outcome is determined by chance).
    • Examples:
      • 抛一枚硬币, 结果可能正面(或反面)朝上 (e.g., tossing a coin, its outcome maybe Heads or Tails).
      • 掷一颗骰子, 可能出现的点数 (rolling a die).
      • 向同一目标射击, 各次弹着点都不相同 (target practice).

• 概率统计的起源 (Origin of Probability and Statistics)

  • Originated in the mid-17th century due to the need to study large statistical data in areas like error estimation, demographic statistics, maritime risk, and life insurance.
  • Led to the development of a mathematical discipline for studying the regularity of large numbers of random phenomena.

• 历史上的第一个概率论问题 (The first question of probability theory in history)

  • 概率论最早是从赌博 (博弈) 游戏开始的 (The origin of probability comes from gambling).
  • Blaise Pascal (1623-1662):