Marginal Formulae

Question 1

What is the formula for marginal pdf of x, a discrete random variable?

Answer 1

Σ_Ryf(x,y)

Question 2

What is the formula for marginal pdf of y (discrete)?

Answer 2

Σ_Rxf(x,y)

Question 3

What is the marginal expectations of x for discrete random variable?

Answer 3

E(X) = Σ_Rx Σ_Ry x • f(x,y)

Question 4

What is the marginal expectation of y for discrete random variable?

Answer 4

E(Y) = Σ_Rx Σ_Ry y • f(x,y)

Question 5

What is the formula for marginal (probability) distribution of x for continuous random variable?

Answer 5

∫_Ryf(x,y) dy

Question 6

What is the formula for marginal (probability) distribution of y for continuous random variable?

Answer 6

∫_Rxf(x,y) dx

Question 7

When are random variables x and y independent?

Answer 7

1. f(x,y) = f(x) • f(y)
2. F(x,y) = F(x) • F(y)
3. E(x,y) = E(x) • E(y)
4. Cov(x,y) = 0

Question 8

What is the formula for conditional expectation of x (discrete)?

Answer 8

E(x|y) = Σ_RxX• f(x,y)/f(y)
Where f(y) is the marginal density function of y.