stats base

Question 1

pdf transformation

Answer 1

Y=g(X) X=g-1(Y), fy=fx(g-1(Y) |d/dy g-1(Y)

Question 2

exp transformation

Answer 2

Y=g(X) X=g-1(Y), EY= int g(X) fx imp for moments!

Question 3

variance aX+bY

Answer 3

a^2varX+b^2varY+ 2abCov

Question 4

CovXY

Answer 4

E(XY)-EY*EX

Question 5

moment gen function

Answer 5

int e^(tx)f(x) t=moment?

Question 6

Marginal densities and conditional and conditional expecation

Answer 6

fx=int f(x,y) dy
fx|y = f(x,y)/fy
eY|x=x = int y*fY|X

Question 7

E(XY)

Answer 7

int int f(x,y)xy

Question 8

Correlation

Answer 8

cov/(sqrt(varX*varY)

Question 9

Chi2 how get

Answer 9

sum of standard normals squared

Question 10

Sum of 2 chi squares

Answer 10

chi square n+m if indep

Question 11

2X/theta X exponential and with sum

Answer 11

Chi squared 2, 2n

Question 12

Exp and variance chi squared

Answer 12

n, 2n

Question 13

t how get

Answer 13

Z/sqrt(Chi/deg) = t deg of chi

Question 14

F how get and deg

Answer 14

ratio chi_m/deg / chi_n/deg deg m, n

Question 15

t^2

Answer 15

F 1,n

Question 16

Distribution Xbar from normal

Answer 16

N(mu, sigma/n)

Question 17

(n-1)S^2/sigma^2

Answer 17

chi n-1

Question 18

Xbar-mu/(S/sqrt(n))

Answer 18

t n-1

Question 19

CLT

Answer 19

Xbar-mu/sigma/(sqrt n) tends to Z

Question 20

Sum of squared integers

Answer 20

n(n+1)(2n+1)/6

Question 21

Gamma function

Answer 21

F(n) = (n-1)!

Question 22

Var(sumX)

Answer 22

sum Var(x)

Question 23

pdf max

Answer 23

n(x^n-1)/theta^n