Applied Statistics and Probability for Engineers

652 APPENDIX A STATISTICAL TABLES AND CHARTS

Table I Summary of Common Probability Distributions

Probability Section

Name Distribution Mean Variance in Book

Discrete

Uniform 3-5

Binomial np 3-6

Geometric 3-7.1

Negative binomial 3-7.2

Hypergeometric np, 3-8

Poisson 3-9

Continuous

Uniform 4-5

Normal ^2 4-6

Exponential 4-8

Erlang 4-9.1

Gamma 4-9.2

Weibull 4-10

Lognormal e^2  

 4-11

2

1 e^

2

e  

 12

(^122)
x 22
exp a
3 ln 1 x 2  42
2
2
b
^2 c a 1
1

bd
2
0 x, 0, 0
^2 ^ a 1

2

 a 1 b
1

b


a
x

b
 1
e^1 x^ ^2

,
r  r ^2
xr^1 e^ x
 1 r 2
, 0x, 0r, 0
r  r ^2
rxr^1 e^ x
1 r 12!
, 0x, r1, 2,...
e^ x, 0x, 0 1  1 ^2
x, , 0
1
 12
e
121 x 22
1 b a 22
12
1 b a 2
2
1
b a
, axb
e^ x
x!
, x0, 1, 2,... , 0
min 1 K, n 2 , KN, nN
xmax 1 0, n N K 2 , 1,...
where p
K
N
np 11 p 2 a
N n
N 1
b
a
K
x
b a
N K
n x
b
a
N
n
b
xr, r 1, r 2,... , 0p 1
a r p r 11 p 2 p^2
x 1
r 1
b 11 p 2 x^ rpr
x1, 2,... , 0p 1
11 p 2 x^1 p, 1 p 11 p 2 p^2
x0, 1,... , n, 0p 1
a np 11 p 2
n
x
b px 11 p 2 n^ x,
1 b a 1221
12
1 b a 2
2
1
n, ab
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