Discrete Random Variables

Question 1

What is the formula for the mean of a discrete random variable?

Answer 1

Sigma(x_ip_i)

Question 2

What is the formula for variance?

Answer 2

Sigma(x_i²p_i) - Sigma(x_ip_i)²

Question 3

How do operations affect expectation?

Answer 3

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

Question 4

How do operations affect variance?

Answer 4

Var(aX + b) = a²Var(X)

Question 5

How can the expectations of two random variables be combined?

Answer 5

E(X₁+ X₂) = E(X₁) + E(X₂)

E(X₁- X₂) = E(X₁) - E(X₂)

Question 6

How can the variance of two random variables be combined?

Answer 6

Var(X₁+ X₂) = Var(X₁) + Var(X₂)

Var(X₁- X₂) = Var(X₁) + Var(X₂)

Question 7

What is the formula for the mean in discrete uniform distribution?

Answer 7

1/2(n+1)

Question 8

What is the formula for the variance in discrete uniform distribution?

Answer 8

1/12(n²-1)