Deck 2 - Probability and Stats Refresher

Question 1

definition of expected value

Answer 1

probability-weighted average of a random variable’s outcomes

Question 2

two key EV rules

Answer 2

1. E(aX+b)=aE[X]+b
2. E(X+Y)=E[X]+E[Y]

Question 3

variance of linear transform

Answer 3

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

Question 4

variance of a sum

Answer 4

Var(aX+bY)=a^2Var(X)+b^2Var(Y)+2abCov(X,Y)

Question 5

when does Cov(X,Y)=0?

Answer 5

when x and y are independant (independence ⇒ zero covariance)

Question 6

correlation range and meaning

Answer 6

between -1 and 1 measuring linear association strength/direction

Question 7

why is covariance scale-dependant

Answer 7

it changes with units; correlation is unit-free

Question 8

sampling mean variance for n i.i.d (independent and identically distributed) observations

Answer 8

Var( X̄ )=Var(X)/n

The standard expression for how the variance of the sample mean decreases as the sample size ( n ) increases.

Question 9

median vs mode

Answer 9

median splits probability mass at 0.5; mode is most likely value