Flashcards in Multivariate distribution theory Deck (11):

1

## When are a pair of continuous random variables independent?

### If f_xy_(x,y) = fx(x)fy(y)

2

## What is the formula for the covariance?

### E[XY] - E[X]E[Y]

3

## What is the formula for the correlation coefficient?

### Cov(X,Y)/sqrt(Var(X)Var(Y))

4

## formula for E[XY]

### double integral of[ xyf(x,y)dydx] over the region R squared

5

## If X and Y are independent then what does this mean for the covariance?

### the covariance is equal to 0

6

## var[X|Y] =

### E[(X - E[X|Y])^2 | Y]

7

## E[E[X|Y]]

### E[X]

8

## F_X|Y_y(x) =

### F_X,Y(x,y)/F_Y(y)

9

## F_X(x)=

### integral over range of y for F_X,Ydy

10

## E[X|Y = y] =

### integral over range of (xf_X|Y=y_(x))dx

11