Fundamentals of Probability and Statistics for Engineers

3.3 For pX (x) and f (^) X (x) in Figure 3.19(a) and 3.19(b) respectively, sketch roughly in
scale the corresponding PDF FX (x) and show on all graphs the procedure for
finding P(2 < X < 4).
3.4 For each part, find the corresponding PDF for random variable X.
(a) Case 1:
(b) Case 2:
(c) Case 3:
3.5 The pdf of X is shown in Figure 3.20.
(a) Determine the value of a.
(b) Graph FX (x) approximately.
(c) Determine P(X 2).
(d) Determine P(X 2 X 1).
3.6 The life X, in hours, of a certain kind of electronic component has a pdf given by
Determine the probability that a component will survive 150 hours of operation.
(a)
123
0.6
0.2
x
pX(x)
(b)
fX(x)
4
x
Figure 3. 19 The probability mass function, pX (x), and probability density function,
fX (x), for Problem 3.3
68 Fundamentals of Probability and Statistics for Engineers
fX…x†ˆ^0 :^1 ; for 90x<^100 ;
0 ; elsewhere:

fX…x†ˆ 02 …;^1 elsewherex†; for 0: x<^1 ;

fX…x†ˆ
1
… 1 ‡x^2 †
; for1<x< 1 :

j
fX…x†ˆ
0 ; forx< 100 ;
100
x^2
; forx 100 :
8
<
: