Introduction to Probability · 免费预览
给定随机变量的条件期望与亚当定律
将给定 Y 时 X 的期望视为随机变量、从 Y 的函数这一视角来看，以及亚当定律——给定 Y 时 X 的期望的期望等于 X 的期望——为投影与预测提供强大支撑。
1. The random variable that knows more
The random variable that knows more
2. Adam's law
Adam's law
3. The best predictor
The best predictor
4. Which is the random variable?
Which of these quantities is a random variable?
5. Compound expectation
Claims arrive at mean count 8 per period, each averaging 250 dollars independently. What is the expected total claims per period?
6. A die-slice average
Given Y = 4, X is Uniform on 1 through 4. What is E(X given Y = 4)? Enter a decimal like 2.5.
7. Adam's law applied
E(X given Y) = 2Y and Y takes values 1 and 3 with equal probability. What is E(X)? Enter an integer.
8. Two-step function
Given N = n, E of X is n squared. N is 2 with probability 0.7 and 3 with probability 0.3. What is E(X)? Enter like 7.9.
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.