stats Flashcards
E(x) =
sum of probability * X
var x
E(x^2) - E(x)^2
Y = Ax +B
var x = e x =
A E(x) + B
A^2 Var X
E(x + y)
E(x) + E(Y)
E(xy)
sum of XYprobability
poisson approximation requirements
high n small p
poisson requirements
singly , independant
and at a constant average rate
equal to or less than geo
1-(1-P)^x
equal to or greater than geo
(1-P)^x-1
for greater than or less than for negative binomial
manipulate to use binomial
Hypothesis test
value of population parameter is tested against what vaue it takes if h0 is rejected
critical region
range of values that would cuase rejection of null hypothesis
z=
x - u / sq root (variance over sample size)
null hyp for testing distribution
distribution is uitbale
alternate hypothesis for testing distribution
distribution not suitable
Degrees of free dom
number of cells -1 ( -1 more if probability is worked out)
work out p for geometric
number of succeses over number of trials
work out p for binomial
sum of X * frequency / (number of x * number of observation)
poissson estimated p
sum of X * frequency / number of observation
generateing function
probabilty times by t^x
Gx(1) =
1
Ex =
G dash x (1)
var x =
g ouble dash of x (1) + g dash of x (1) - (g dash of x (1))^2
generating z = x + y
G of z(t) = Gx(t) x Gy(t)
how to find generatinf function from possion first priciples
write first few terms in expoential form
factorise out e^-lamda
rest of inside bracket is mclaurin series
function for binomial
sum of probabilty of all terms
= binomail expansion
Gxn dash (0) =
n!P(X=n)
type 1 error =
size = when null is rejcted but it is true
tye 2 error =
when null is accepted but null is flase
power =
when null is rejected and null is false
1 - type 2 error
power function
function of parameter theta that wll give probabiltuy that test statisctic will fall into critical egion if theta is true
what happens if type 2 is increased
type 1 decrease
