Introduction to Probability · 免费预览
指示随机变量与基本桥梁
指示函数是概率的基本原子，指示函数的期望就是概率，而按指示函数计数则是通用的技术手段。
1. Indicators and the fundamental bridge
Indicators and the fundamental bridge
2. Counting with indicators
Counting with indicators
3. Patterns, runs, and a Ramsey surprise
Patterns, runs, and a Ramsey surprise
4. The fundamental bridge
Which identity is the fundamental bridge between probability and expectation?
5. Empty boxes
10 balls drop independently into 4 equally likely boxes. What is the expected number of empty boxes?
6. Birthday pair expectation
In a room of 25 people with uniform independent birthdays over 365 days, the expected number of matching pairs is Binomial(25,2) times 1/365. Enter that value rounded to two decimals, like 0.85.
7. Indicator variance
An event A has probability 0.2. What is the variance of its indicator? Enter a decimal like 0.16.
8. Local maxima
A random permutation of 1 through 12 has how many expected interior local maxima, at one third of the 10 interior positions? Enter like 3.33.
9. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.