Multivariate distribution theory Flashcards Preview

MAS223 > Multivariate distribution theory > Flashcards

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

What is important about the t-distribution that makes it useful?

We can use the T distribution even without knowing values for μ or σ^2