Fundamentals of Probability and Statistics for Engineers

The probability we are seeking is thus the volumeunder this surface over an
appropriate region R. For this problem, the region R is given by

and is shown in Figure 3.16 in the (x,y) plane.
The volume of interest can be found by inspection in this simple case.
Dividing R into three regions as shown, we have

P(they will meet) P X Y 10

ab

x

fX(x)

1

b–a

Figure 3. 14 A uniform density function, fX (x)

fXY(x,y) y

060

60

3600

x

1

Figure 3. 15 The joint probability density function fX Y (x,y), for Example 3.7

58 Fundamentals of Probability and Statistics for Engineers

R:jXYj 10

ˆ…j j †

ˆ‰ 2 … 5 †… 10 †‡ 10



2

p

… 50



2

p

†Š= 3600 ˆ

11

36