Introduction to Probability · 免费预览
期望与线性性
随机变量的长期平均值（通过将取值乘以概率后求和计算得到），以及无需借助分布就能解决困难问题的线性性质。
1. Definition and the seesaw picture
Definition and the seesaw picture
2. Linearity
Linearity
3. Symmetry and indicators
Symmetry and indicators
4. Linearity with dependence
X and Y are dependent random variables with E(X) = 3 and E(Y) = 2. What is E(X + Y)?
5. The hat check expectation
In the matching problem with n people and n hats shuffled randomly, the expected number of people who retrieve their own hat equals what?
6. A die roll's expectation
A fair six-sided die is rolled once. What is E(roll)? Enter a decimal like 3.5.
7. Two dice sum
Two fair dice are rolled and summed. Using linearity with each die worth 3.5, what is the expected sum? Enter an integer.
8. Aces in a hand
A 5-card hand is dealt from a standard 52-card deck. By indicators, the expected number of aces is 4 times 5/52. Enter that value as a fraction in lowest terms, then report the numerator.
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.