stats Flashcards
var(x)
e(x^2)-e(x)^2
e(ax+b)
ae(x)+b
var(ax+b)
a^2var(x)
conditions for poisson
- independently
- singly
- constant average rate
mean and var of poisson
lambda
conditions for approximating binomial as poisson
- n is large
- p is is small
how to approximate binomial to poisson
lambda = np
what is geo used for
number of trials for one success
geo P(X=x)
p(1-p)^x-1
geo P(X<=x)
1-(1-p)^x-1
geo P(X>x)
(1-p)^x
geo P(x>=x)
(1-p)^x-1
mean of geo
1/p
var of geo
(1-p)/p^2
what is -ve B used for
number of trials to get a set number of successes
-ve B P(X=x)
x-1Cr-1 p^r(1-p)^x-r
mean of -ve B
r/p
var of -ve B
r(1-p)/p^2
CLT
sample size of n from any dist with mean mu and var sigma^2 then mean x is canr be distributed N(mu, sigma^2/n)
goodness of fit formula
(Oi-Ei)^2/Ei
degrees of freedom
cells-constraints (at least 1)
if X^2 exceeds critical val
reject null
Ei for contingency tables
(row tot x column tot)/total
if P is less than significance level
reject Ho
how is significance leveln affected in 2 tailed test
half sig level given
what ahppens if a val is in critical region
reject Ho
pgf of binomial
Gx(t)=(1-p+pt)^n
pgf of poisson
Gx(t)=e^lambda(t-1)
pgf of geo
Gx(t)= pt/1-(1-p)t
pgf of -ve B
Gx(t)=(pt/1-(1-p)t)^r
E(x) pgf
G’x(1)
Var(X) pgf
G’‘x(1)+G’x(1)-(G’x(1))^2
Gz(t) where Z=X+Y
Gy(t) x Gx(t)
Gy(t) where Y=aX+b
t^bGx(t^a)
type 1 error
reject null when true
same as sig level
type 2 error
accept null when false
size
p(type 1)
power
1-p(type 2)
