2.2.4 Variance

Question 1

what is a raw moment?

Answer 1

a moment based on the actual value of X. i.e. E(X)

Question 2

what is a central moment?

Answer 2

a moment based on the difference between the value of X and the mean of X.
i.e. E[(X-(μ))^k] is the kth central moment

Question 3

what is the variance?

Answer 3

the 2nd certain moment. quantity that describes the degree to which X
deviates from its mean.

i.e.
σ^2 = Var[X] = E[(X-(μ))^2]

Question 4

what does larger and smaller variance mean?

Answer 4

A larger variance means the observations are more dispersed, or more spread out from the mean and the distribution is more dense around it’s mean

A smaller variance means the observations are closer to the mean it’s more spread around it’s mean.

Question 5

whats the shorthand way to calc Var[X]?

Answer 5

Var[X] = E[X^2] - (E[X])^2

Question 6

what is the variance of a constant equal?

Answer 6

0. DUH

Question 7

what does Var[aX+b] equal?

Answer 7

Var[aX+b] = a^2 * Var[X]