Introduction to Probability · free preview
Conditional Expectation Given a Random Variable and Adam's Law
E of X given Y as a random variable, the function-of-Y view, and Adam's law E of E of X given Y equals E of X powering projection and prediction.
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.
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