Introduction to Probability · 免费预览
独立性与作为概率的条件概率
在条件化的世界中进行代数运算、独立性的定义与陷阱，以及条件独立性与之对应的无条件版本的比较。
1. Algebra inside the conditioned world
Algebra inside the conditioned world
2. Independence
Independence
3. Working definitions and a classical application
Working definitions and a classical application
4. Spotting independence numerically
P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.3. Are A and B independent?
5. Dependent coins after evidence
Two fair coins are tossed. Given that exactly one shows heads, what is the status of the events first coin heads and second coin heads?
6. Chain rule for a full house of aces
Cards are drawn one by one without replacement from a shuffled deck. What is the probability the first two cards are both aces? Write it as a fraction in lowest terms and enter the denominator.
7. Pairwise but not mutual
Two fair coins are tossed; A is first coin heads, B is second coin heads, C is the coins match. Compute P(A and B and C). Independence of all three would give 1/8; the true value as a fraction has what numerator?
8. Sensor fusion
A machine is up with probability 0.9. Two conditionally independent sensors each report correctly with probability 0.95. Both read UP. Rounded to two decimals, what is the probability the machine is up? Enter like 1.00.
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.