Continuous Random Variables (Further)

Question 1

CRV ∫ f(x)

Answer 1

∫ f(x) = 1

Question 2

Median of CRV

Answer 2

Integrate from infinity to 1/2

Question 3

CRV E(X)

Answer 3

E(X) = ∫ x f(x)

Question 4

CRV Var(X)

Answer 4

Var(X) = ( ∫ x^2 f(x) ) - (E(X))^2

Question 5

CRV E(g(X))

Answer 5

E(g(X)) = ∫ g(x) f(x)
E(g(X)) = aE(X) + b      (if g(x) is linear)

Question 6

CRV Var(aX = b)

Answer 6

Var(aX = b) = a^2 Var(X)