Moments

Question 1

Expected Value

Answer 1

Mean (first moment)

Denoted by E[X]

Question 2

E[X] =

for discrete, continuous, and using survival function

Answer 2

Discrete: E[X] = ∑ x ⋅ Pr(X=x)
Discrete Survival: E[X] = ∑ Pr(X>x)

Continuous: E[X] = ∫ x ⋅ fx(x)
*Limits are bounds of function
Continuous Survival: E[X] = ∫Sx(x)
*Limits are bounds of function

Question 3

Expected Value of other functions

Answer 3

Discrete: E[g(X)] = ∑ g(x) ⋅ Pr(X=x)
Continuous: E[X] = ∫ g(x) ⋅ fx(x)