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3
Probability Models
3.8
The Cauchy Distribution:
𝖢𝖺𝗎𝖼𝗁𝗒
4
Univariate Transformations
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3.9
Summary of probability distributions
Name
Abbrev.
Disc/Cts
Values
Discrete uniform
𝖴𝗇𝗂𝖿
(
0
,
m
)
D
0
,
1
,
…
,
m
Bernoulli
𝖡𝖾𝗋𝗇
(
θ
)
D
0
,
1
Binomial
𝖡𝗂𝗇
(
n
,
θ
)
D
0
,
1
,
…
,
n
Geometric
𝖦𝖾𝗈𝗆
(
θ
)
D
0
,
1
,
2
,
3
,
…
Poisson
𝖯𝗈𝗂𝗌𝗌𝗈𝗇
(
λ
)
D
0
,
1
,
2
,
3
,
…
Uniform
𝖴𝗇𝗂𝖿
(
a
,
b
)
C
[
a
,
b
]
Exponential
𝖤𝗑𝗉
(
β
)
C
[
0
,
∞
)
Gamma
𝖦𝖺𝗆
(
α
,
β
)
C
[
0
,
∞
)
Beta
𝖡𝖾𝗍𝖺
(
α
1
,
α
2
)
C
[
0
,
1
]
Weibull
𝖶𝖾𝗂𝖻
(
α
,
β
)
C
[
0
,
∞
)
Normal
𝖭
(
μ
,
σ
2
)
C
(
-
∞
,
∞
)
Cauchy
𝖢𝖺𝗎𝖼𝗁𝗒
C
(
-
∞
,
∞
)