Fundamentals of Probability and Statistics for Engineers

Table 7.1

Summary of continuous distributions

Distribution

Probab

ility density function

Parameters

M ean and variance

236 Fundamentals of Probability and Statistics for Engineers

Uniform

fX

"x

)

ˆ

1

b



a

,

a



x



b

a,

b

>

a

a

‡

b

2

",

b



a)

2

12

Normal "Gaussian)

fX

"x

)

ˆ

1

"2

)

1/2



exp



"x



m

(^2) )
2 
2

,
1
<
x
<
1
m
,>
0
m
,
2
Lognormal
fY
"y
)ˆ
1
y
ln
Y
"2
)
1/2
exp

1
2 
2 ln
Y


ln
2
y Y

,y

0
Y

0,
ln
Y

0
Y
exp
(^2) ln
Y 2

,
m
2 [ exp "Y
(^2) ln
Y
)
1]
Gamma
fX
"x
)
ˆ
 "
x)

1 exp "

x),
x

0
>
0,
>
0
 
,
^2 
Exponential
fX
"x
)
ˆ

exp "

x),
x

0
>
0
1 
,
(^12) 
Chi-squared
fX
"x
)
ˆ
1
 2
/2
"
/2)
"x
/2)
^1
exp "
x
/2),
x

0

ˆ
positive integer
,2