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
within one s of m
within two s of m
95.45% 47.725 %
within three s of m
Poisson expected value E(X)
Poisson variance Var(X)
the distribution of one variable given the other
distribution of one variable regardless of the value of the other
probability of A and B = probability of A times probability of B given A (or vice versa)
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
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
assumes non-negative values only
William Goset; student's t
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
beta distribution pdf
beta distribution a=b=1
The uniform distribution is a special case of the beta distribution where a=b=1.
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
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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