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poisson pmf

center of gravity

to change any normal distribution to standard normal distribution

subtract m and divide by s

if you change m

it just moves the curve; z doesn't change

if you change s

it just scales the curve; z doesn't change

z

within one s of m

68.27% 34.135%

within two s of m

95.45% 47.725 %

within three s of m

99.73% 49.865%

Poisson expected value E(X)

Poisson variance Var(X)

e

≈ 2.71828

conditional distribution

the distribution of one variable given the other

marginal distribution

distribution of one variable regardless of the value of the other

multiplication rule

probability of A and B = probability of A times probability of B given A (or vice versa)

addition rule

probability of A or B = probability of A + probability of B - probability of A and B

uniform distribution expected value E(X)

pdf yielding normal distribution

pdf yielding standard normal distribution

F(-z)

1-F(z)

F(z) - F(-z)

2 F(z) - 1

z for 99%

2.33

z for 95%

1.645

z for 90%

1.28

z for 80%

0.84

z for 75%

0.675

z for 70%

0.55

z for 60%

0.25

z for 50%

0

z for 40%

-0.25

z for 30%

-0.55

z for 25%

-0.675

z for 20%

-0.84

z for 10%

-1.28

z for 5%

-1.645

z for 1%

-2.33

Theorem 3.6.1 p 220

If you add two independent random variables, the sum is a random variable distributed as the sum of the means, the sum of the standard deviations

Chi-square distribution

assumes non-negative values only

t distribution

William Goset; student's t

F distribution

Fisher distribution; Ronald Fisher; for two independent random variables each with Chi-square distribution p225

exponential distribution density function

exponential distribution function

gamma distribution density function

gamma function

beta distribution pdf

beta distribution a=b=1

The uniform distribution is a special case of the beta distribution where a=b=1.

beta distribution

non-parametric or distribution-free inference statistical inference where results obtained are general and are applicable to any arbitrary distribution; e.g. % of defective units in a manufacturing process, % of errors made in data entry, and % of fans satisfied with the performance of the team they support

beta mean

beta variance

Chi-square distribution is a special case of the

Gamma distribution where a= n/2 and l=1/2; n is number of degrees of freedom.

lognormal

p 234

gumbel

p 236

weibull

p238

frechet

p 241

maxwell

p 241

pareto

p 242