1
Continuous Random Variables
Reading: Chapter 3.1 – 3.8
Homework: 3.1.2, 3.2.1, 3.2.4, 3.3.2, 3.3.7,
3.4.4, 3.4.5, 3.4.9, 3.5.3., 3.5.6,
3.6.1, 3.6.6, 3.7.1, 3.7.3, 3.7.11, 3.8.1.
G. Qu
ENEE 324 Engineering Probability
2
Cumulative Distribution Function
CDF of a random variable X is: F
X
(x) = P[X≤x]
X is a continuous random variable if F
X
(x) is
continuous. (the range of X contains a
continuous interval)
Example:
X: a random integer between 0 and 4.
S
X
={0,1,2,3,4}
P
X
(x) = 0.2 for x=0,1,2,3,4 and 0 otherwise
F
X
(x) is an non-decreasing piece-wise constant function that is not
continuous at x=0,1,2,3,4
Y: a random real number between 0 and 4.
S
Y
=[0,4] is a continuous region, not a countable set.
F
Y
[y] = P[Y≤y] = ?
P
Y
[Y=y] = ?
>
≤
≤
<
=
4
1
4
0
4
/
0
0
)
(
y
y
y
y
y
F
Y