Digital Signal Processing Reference
In-Depth Information
4
3
2
1
0
0
100
200
300
400
500
600
700
800
900
1000
n
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
cells
p
2ln
X
Fig. 2.81
Transformation
Y ¼
,
X
is uniform in [0, 1]
2.11 Questions
Q.2.1. What is the unit of a random variable?
Q.2.2. In the definition of random variables, we defined the real random variable.
Does this mean that the random variable can also be complex?
Q.2.3. Do we only label the outcome
s
i
, from the sample space, with a single
number?
Q.2.4. What is the domain of a random variable, keeping in mind that the random
variable is a function?
Q.2.5. Are there conditions in which a function can be a random variable?
Q.2.6. Is the definition of a random variable “correct” in the rigid mathematical
meaning?
Q.2.7. Does mapping
X
(
s
i
) to the real
x
-axis present a complete description of the
sample space
S
?
Q.2.8. Can two different variables have the same distribution function?
Q.2.9. Is it correct to write the distribution as
F
X
(
x
)
¼ P
{
X < x
}, instead of
F
X
(
x
)
¼ P
{
X x
}?
Q.2.10. Is the PDF of a discrete random variable a discrete function in itself?
Q.2.11. The distribution function for the discrete, continuous, and mixed random
variables is given as
F
X
(
x
). Does this mean that the distribution is a
continuous function in all cases?
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