2.2.1 Expected Value

Question 1

how do you take the n-th moment of a discrete random variable?

Answer 1

E(X^n) = SUM(x^n * P(X=x))

Question 2

how do you take the n-th moment of a continous random variable?

Answer 2

E(X^n) = integral with bound of where the function is defined(x*n * f(x))

Question 3

what are important properties of expectation?

Answer 3

E(c) = c
E(cg(X)) = cE(g(X))
E(X_1, … , X_n) = E(X_1) + … + E(X_n)

Question 4

what is conceputally happening when you get the nth moment?

Answer 4

you weigh every possible value to the nth power with it’s probability giving you how much it “spreads” from a reference point