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poisson pmf

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center of gravity

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to change any normal distribution to standard normal distribution

subtract m and divide by s

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if you change m

it just moves the curve; z doesn't change

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if you change s

it just scales the curve; z doesn't change

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z

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within one s of m

68.27% 34.135%

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within two s of m

95.45% 47.725 %

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within three s of m

99.73% 49.865%

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Poisson expected value E(X)

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Poisson variance Var(X)

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conditional distribution

the distribution of one variable given the other

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marginal distribution

distribution of one variable regardless of the value of the other

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multiplication rule

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

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addition rule

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

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uniform distribution expected value E(X)

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pdf yielding normal distribution

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pdf yielding standard normal distribution

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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

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Chi-square distribution

assumes non-negative values only

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t distribution

William Goset; student's t

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F distribution

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

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exponential distribution density function

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exponential distribution function

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gamma distribution density function

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gamma function

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beta distribution pdf

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beta distribution a=b=1

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

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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

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beta mean

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beta variance

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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.

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