Ch. 8 Expectation

Question 1

Linearity of Expectation

Answer 1

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

E(X + Y) = E(X) + E(Y)

Question 2

Var(X) =

Answer 2

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

Question 3

Cov(X, Y) =

Answer 3

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

Question 4

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

Answer 4

E(X | Y = Y(ω))

Question 5

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

Answer 5

E(E(X | Y))

Question 6

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

Answer 6

E(X)E(Y)

Question 7

Markov’s Inequality:

Answer 7

P (X ≥ a) ≤ E(X) / a

Question 8

Chebyshev’s Inequality:

Answer 8

P( |X-E(X)| ≥ a) ≤ Var(X) / a^2