stats Flashcards by Rebecca Daffin | Brainscape

Q

var(x)

A

e(x^2)-e(x)^2

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Q

e(ax+b)

A

ae(x)+b

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Q

var(ax+b)

A

a^2var(x)

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Q

conditions for poisson

A

independently
singly
constant average rate

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Q

mean and var of poisson

A

lambda

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Q

conditions for approximating binomial as poisson

A

n is large
p is is small

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Q

how to approximate binomial to poisson

A

lambda = np

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Q

what is geo used for

A

number of trials for one success

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Q

geo P(X=x)

A

p(1-p)^x-1

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Q

geo P(X<=x)

A

1-(1-p)^x-1

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Q

geo P(X>x)

A

(1-p)^x

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Q

geo P(x>=x)

A

(1-p)^x-1

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Q

mean of geo

A

1/p

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Q

var of geo

A

(1-p)/p^2

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Q

what is -ve B used for

A

number of trials to get a set number of successes

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Q

-ve B P(X=x)

A

x-1Cr-1 p^r(1-p)^x-r

Q

mean of -ve B

A

r/p

Q

var of -ve B

A

r(1-p)/p^2

Q

CLT

A

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)

Q

goodness of fit formula

A

(Oi-Ei)^2/Ei

Q

degrees of freedom

A

cells-constraints (at least 1)

Q

if X^2 exceeds critical val

A

reject null

Q

Ei for contingency tables

A

(row tot x column tot)/total

Q

if P is less than significance level

A

reject Ho

Q

how is significance leveln affected in 2 tailed test

A

half sig level given

Q

what ahppens if a val is in critical region

A

reject Ho

Q

pgf of binomial

A

Gx(t)=(1-p+pt)^n

Q

pgf of poisson

A

Gx(t)=e^lambda(t-1)

Q

pgf of geo

A

Gx(t)= pt/1-(1-p)t

Q

pgf of -ve B

A

Gx(t)=(pt/1-(1-p)t)^r

Q

E(x) pgf

A

G’x(1)

Q

Var(X) pgf

A

G’‘x(1)+G’x(1)-(G’x(1))^2

Q

Gz(t) where Z=X+Y

A

Gy(t) x Gx(t)

Q

Gy(t) where Y=aX+b

A

t^bGx(t^a)

Q

type 1 error

A

reject null when true
same as sig level

Q

type 2 error

A

accept null when false

Q

size

A

p(type 1)

Q

power

A

1-p(type 2)