Stats Review (Equations/Homework)

Question 1

Expected Value (HW 1 P. 1)

Answer 1

E(X)=x1f(x1) + x2f(x2) + x3f(x3)…

{x1,x2,x3} proportion of whole

{f(x1),f(x2),f(x3),…} Value of proportions

Question 2

Cumulative distribution function (HW 2 P.2)

Answer 2

F(x) ≡ P(X ≤ x)

For any number c, P(X > c) = 1 − F(c)

For any numbers a < b, P(a < X ≤ b) = F(b) − F(a)

Question 3

Variance

Answer 3

Var(X) ≡E[(X − μ)^2]

μ = mean

Question 4

Standard Deviation

Answer 4

sd(X) or σX

sd(X) ≡ √ Var(X)

Question 5

Variance with constants

Answer 5

Var(aX + bY) =a2Var(X) + b2Var(Y) + 2abCov(X, Y)

Question 6

Covariance

Answer 6

Cov(X, Y) ≡E[(X − μX )(Y − μY )]