stats

Question 1

E(x) =

Answer 1

sum of probability * X

Question 2

var x

Answer 2

E(x^2) - E(x)^2

Question 3

Y = Ax +B

var x = 
e x =

Answer 3

A E(x) + B

A^2 Var X

Question 4

E(x + y)

Answer 4

E(x) + E(Y)

Question 5

E(xy)

Answer 5

sum of XYprobability

Question 6

poisson approximation requirements

Answer 6

high n small p

Question 7

poisson requirements

Answer 7

singly , independant

and at a constant average rate

Question 8

equal to or less than geo

Answer 8

1-(1-P)^x

Question 9

equal to or greater than geo

Answer 9

(1-P)^x-1

Question 10

for greater than or less than for negative binomial

Answer 10

manipulate to use binomial

Question 11

Hypothesis test

Answer 11

value of population parameter is tested against what vaue it takes if h0 is rejected

Question 12

critical region

Answer 12

range of values that would cuase rejection of null hypothesis

Question 13

z=

Answer 13

x - u / sq root (variance over sample size)

Question 14

null hyp for testing distribution

Answer 14

distribution is uitbale

Question 15

alternate hypothesis for testing distribution

Answer 15

distribution not suitable

Question 16

Degrees of free dom

Answer 16

number of cells -1 ( -1 more if probability is worked out)

Question 17

work out p for geometric

Answer 17

number of succeses over number of trials

Question 18

work out p for binomial

Answer 18

sum of X * frequency / (number of x * number of observation)

Question 19

poissson estimated p

Answer 19

sum of X * frequency / number of observation

Question 20

generateing function

Answer 20

probabilty times by t^x

Question 21

Gx(1) =

Answer 21

1

Question 22

Ex =

Answer 22

G dash x (1)

Question 23

var x =

Answer 23

g ouble dash of x (1) + g dash of x (1) - (g dash of x (1))^2

Question 24

generating z = x + y

Answer 24

G of z(t) = Gx(t) x Gy(t)

Question 25

how to find generatinf function from possion first priciples

Answer 25

write first few terms in expoential form

factorise out e^-lamda

rest of inside bracket is mclaurin series

Question 26

function for binomial

Answer 26

sum of probabilty of all terms

= binomail expansion

Question 27

Gxn dash (0) =

Answer 27

n!P(X=n)

Question 28

type 1 error =

Answer 28

size = when null is rejcted but it is true

Question 29

tye 2 error =

Answer 29

when null is accepted but null is flase

Question 30

power =

Answer 30

when null is rejected and null is false

1 - type 2 error

Question 31

power function

Answer 31

function of parameter theta that wll give probabiltuy that test statisctic will fall into critical egion if theta is true

Question 32

what happens if type 2 is increased

Answer 32

type 1 decrease