56 terms

prob April 18, 2012

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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