Introduction to Probability · 免费预览
给定事件的条件期望
在证据内部取平均、由条件分布计算条件期望，以及在两步问题中使用它们。
1. Averaging inside the evidence
Averaging inside the evidence
2. The law of total expectation
The law of total expectation
3. Two-stage problems and shortcuts
Two-stage problems and shortcuts
4. The law of total expectation
A factory's output is 60 percent line A, averaging 10 defects per batch, and 40 percent line B, averaging 25. What is the overall expected defects per batch?
5. A two-stage count
Pick a number N uniformly from 1 to 3, then toss N fair coins and count heads. What is E(heads)?
6. Branch average
E(X given A) = 5, E(X given A complement) = 15, and P(A) = 0.25. What is E(X)? Enter like 12.5.
7. Two-stage coins
Roll a fair die, then flip that many fair coins. Using E of heads given roll k equals k/2, the overall expected heads is 3.5/2. Enter that decimal.
8. Renormalized branch
Given event A, a variable takes value 2 with probability 0.6 and value 8 with probability 0.4 (conditional probabilities). What is E(X given A)? Enter like 4.4.
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.