Introduction to Probability and Statistics for Engineers and Scientists

5.1The Bernoulli and Binomial Random Variables 143

0

0.25

0.20

0.15

0.10

0.05

0.0 123 45678910

Binomial (10, 0.5)

0

0.30

0.25

0.20

0.15

0.10

0.05

0.0 123 45678910

Binomial (10, 0.3)

0

0.30

0.25

0.20

0.15

0.10

0.05

0.0 123 45678910

Binomial (10, 0.6)

FIGURE 5.1 Binomial probability mass functions.

with parameters (10, .01). Hence the probability that a package will have to be replaced is

P{X> 1 }= 1 −P{X= 0 }−P{X= 1 }

= 1 −

(

10

0

)

(.01)^0 (.99)^10 −

(

10

1

)

(.01)^1 (.99)^9 ≈.005