Fundamentals of Probability and Statistics for Engineers

= 1.0

= 0.8

= 0.5

= 0.2

0.0

0.0

1.0

2.0

3.0

4.0

0.2 0.4 0.6 0.8 1.0

x

fX(x)

(a)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

2.0

4.0

6.0

8.0

fX(x)

= 1

= 7

= 2

= 6

= 6

= 2

x

= 7

= 1

= 4

= 4

(b)

Figure 7.13 Beta distribution with: (a) and

and (b) combinations of values of such that 8

222 Fundamentals of Probability and Statistics for Engineers

α α α α α β α β

α

β

α

β

α

β

ˆ2and ˆ 1 :0, ˆ 0 :8, ˆ 0 :5,
ˆ 0 :2; and " , ˆ1,2,...,7) ‡ ˆ