Ch. 8 Expectation Flashcards Preview

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Flashcards in Ch. 8 Expectation Deck (8)
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1

Linearity of Expectation

E(aX + B) = aE(X) + B
E(X + Y) = E(X) + E(Y)

2

Var(X) =

E( (X - E(X))^2 )

3

Cov(X, Y) =

E( (X - E(X)) (Y - E(Y)) )

4

The conditional expectation of X given Y, E(X | Y)(ω) =

E(X | Y = Y(ω))

5

For any 2 discrete RVs X and Y, E(X) =

E(E(X | Y))

6

If X and Y are independent, E(XY) =

E(X)E(Y)

7

Markov's Inequality:

P (X ≥ a) ≤ E(X) / a

8

Chebyshev's Inequality:

P( |X-E(X)| ≥ a) ≤ Var(X) / a^2