Introduction to Probability · 免费预览
贝叶斯定理与全概率公式
对样本空间进行划分，用全概率公式（LOTP）对条件概率取平均，并用贝叶斯定理以赔率形式或借助树形图来反演条件关系。
1. Partitions and the law of total probability
Partitions and the law of total probability
2. Bayes' rule
Bayes' rule
3. Odds and coherency
Odds and coherency
4. Which slice produced it
The gadget problem: factory 1 supplies 60 percent with defect rate 1 percent, factory 2 supplies 40 percent with defect rate 5 percent. A sampled gadget is defective. Which factory is more likely to have produced it?
5. Choosing the denominator
In the rare-condition screening example, which expression is P(condition given positive)?
6. LOTP with both branches
A message is spam with probability 0.3. The filter flags 95 percent of spam and 4 percent of honest mail. What is the probability a random message is flagged? Enter a decimal like 0.32.
7. Odds update
Prior odds of rain are 1 to 4. The forecast model gives a likelihood ratio of 6 for the observed morning clouds, that is, P(clouds given rain) is 6 times P(clouds given dry). What are the posterior odds of rain? Write them as a ratio like 3:2 using the letter x, for example 6:5.
8. Two coins, one drawer
A drawer has two fair coins and one two-headed coin. You pick one at random, flip it, and see heads. What is the probability you hold the two-headed coin? Enter a decimal like 0.5.
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.