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In-Depth Information
TABLE 6.1
Common Probability Distributions
(Continued)
1
Geometric distribution:
0.8
x
p
(
x
) =
p
(1 -
p
)
0.6
0.4
Number of failures before success
in a series of independent Bernoulli
trials
0.2
0
0
1
2
3
4
5
6
7
8
9
10
x
0.6
Uniform distribution:
0.4
1
a
= 3,
b
= 7
f
U
(
x
)
=
,
a
≤
x
≤
b
b
−
a
0.2
Random number
0
0
1
2
3
4
5
6
7
8
9
10
generation (RNG)
x
0.8
Normal distribution:
µ , σ=
=
1/ 2
0.6
2
1
⎡
(
x
−
µ
)
⎤
f
(
x
)
=
exp
−
⎣
⎦
N
2
2
π
σ
2
σ
0.4
µ=0,σ =1
0.2
µ=0,σ=2
Natural phenomena of large
population size
0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
2.5
Exponential distribution:
2
−
λ
x
f
(x)
=
λ
e
Exp
λ=2
1.5
1
Reliability models:
Lifetime of a component
Service time
Time between arrivals
λ=1
0.5
λ = 0.5
0
0
1
2
3
4
5
6
7
8
9
10
x
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