Page 75 - Fundamentals of Probability and Statistics for Engineers

58 Fundamentals of Probability and Statistics for Engineers

f (x)
X

1
b – a

x
a b

Figure 3.14 A uniform density function, f (x)

X
f XY (x,y) y

60

1
3600

x
0 60
Figure 3.15 The joint probability density function f XY (x,y), for Example 3.7

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

R : jX Yj 10

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) ˆ j Y j 10†
P X
p  p  11
ˆ‰2 5† 10†‡ 10 2 50 2†Š=3600 ˆ
36

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