Introduction to Probability · free preview
Conditional Variance and Eve's Law
Variance conditioned on information as a random variable, the two-source decomposition Var equals E of Var plus Var of E, and worked predictions.
1. Conditional variance
Conditional variance
2. Eve's law
Eve's law
3. Using the decomposition
Using the decomposition
4. Reading Eve's law
Var(X) = 30, and Var of E(X given Y) = 12. What is E of Var(X given Y)?
5. What the between-term measures
In Eve's law, a LARGE Var of E(X given Y) means what?
6. Conditional variance shortcut
Given Y = 2, X has E = 5 and E of X squared = 29. What is Var(X given Y = 2)? Enter an integer.
7. Eve's law two branches
Branch A has probability 0.5, mean 10, variance 1; branch B has probability 0.5, mean 20, variance 4. The overall mean is 15. Compute the between-term Var of E(X given branch). Enter like 25.
8. Compound variance
N has mean 10 and variance 10; each X has mean 2 and variance 3. For S = X_1 + ... + X_N, compute E(N)Var(X) + Var(N)(E X)^2. Enter an integer.
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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