PROBABILITY, STATISTICS,
AND RANDOM PROCESSES
FOR ELECTRICAL
ENGINEERING (3RD
EDITION, 2008) –
SOLUTIONS MANUAL –
LEON-GARCIA
Probability, Statistics, and Random Processes for
Electrical Engineering (3rd Edition)
Comprehensive Practice Exam | Questions with Bolded
Correct Answers & Detailed Rationales
Based on the official chapter structure of Leon-Garcia's textbook (Pearson, 2008)
,Chapter 1: Probability Models in Electrical and Computer
Engineering (Questions 1–15)
1. In the context of mathematical modeling, a deterministic model is one in which:
A. Outcomes are governed by chance
B. The future state is completely determined by initial conditions
C. Statistical regularity is the primary tool
D. Random variables are the main building blocks
Rationale: A deterministic model produces the same output for a given set of inputs
every time. There is no randomness or uncertainty in the outcome .
2. The relative frequency of an event approaches a limit as the number of trials
increases. This property is called:
A. The axiomatic approach
B. Statistical regularity
C. Deterministic behavior
D. Conditional probability
Rationale: Statistical regularity refers to the empirical observation that relative
frequencies stabilize as the number of trials grows .
3. Which of the following is NOT a component of building a probability model?
A. Defining the sample space
B. Assigning probabilities to outcomes
C. Proving the central limit theorem
D. Identifying the random experiment
Rationale: Building a probability model involves specifying the experiment, sample
space, and probability assignments. The central limit theorem is a result derived from
probability theory, not a component of model construction .
4. In a packet voice transmission system, the random experiment might involve:
A. The exact time the packet arrives
B. Whether a packet is successfully received or lost
C. The temperature of the transmission medium
D. The color of the packet header
,Rationale: Packet loss/arrival is a classic random experiment in communication systems.
The outcome is uncertain and can be modeled probabilistically .
5. A system consists of two components in series. Each component has reliability
0.9. The system reliability is:
A. 0.9
B. 0.95
C. 0.81
D. 0.99
Rationale: For series systems, reliability = product of individual reliabilities. 0.9 × 0.9 =
0.81 .
6. The axiomatic approach to probability theory requires that probabilities satisfy:
A. Only the normalization condition
B. Non-negativity, normalization, and countable additivity
C. Statistical regularity only
D. Deterministic outcomes only
Rationale: Kolmogorov's axioms: P(A) ≥ 0, P(Ω) = 1, and for disjoint events, P(∪Aᵢ) =
ΣP(Aᵢ) .
7. In reliability calculations, the failure rate function is often denoted as:
A. F(t)
B. h(t) or λ(t)
C. R(t)
D. f(t)
Rationale: The failure rate (hazard rate) function h(t) describes the instantaneous rate of
failure given survival up to time t .
8. A system with components in parallel has reliability:
A. Always less than the least reliable component
B. Always greater than or equal to the most reliable component
C. Equal to the product of component reliabilities
D. Independent of component reliabilities
Rationale: Parallel systems succeed if at least one component works, so system
reliability ≥ max(component reliabilities) .
, 9. Probability models are preferred over deterministic models when:
A. The system is perfectly predictable
B. There is inherent randomness or uncertainty in the system
C. The system has no inputs
D. The system is linear
Rationale: Probability models are appropriate when outcomes are uncertain and
statistical regularity can be observed .
10. Resource sharing systems are often analyzed using probability models because:
A. Resource demands are deterministic
B. Arrival times and service demands are random
C. Resources are infinite
D. There is no uncertainty
Rationale: In resource sharing (e.g., computer networks, telephone systems), user
arrivals and service times are inherently random .
11. The sample space of an experiment is:
A. A single outcome
B. The set of all possible outcomes
C. A subset of outcomes
D. The probability of an outcome
Rationale: The sample space Ω is the set of all possible outcomes of a random
experiment .
12. An event is defined as:
A. A single outcome
B. A subset of the sample space
C. The probability of an outcome
D. The complement of the sample space
Rationale: An event is any subset of the sample space to which a probability can be
assigned .
13. The union of events A and B (A ∪ B) represents:
AND RANDOM PROCESSES
FOR ELECTRICAL
ENGINEERING (3RD
EDITION, 2008) –
SOLUTIONS MANUAL –
LEON-GARCIA
Probability, Statistics, and Random Processes for
Electrical Engineering (3rd Edition)
Comprehensive Practice Exam | Questions with Bolded
Correct Answers & Detailed Rationales
Based on the official chapter structure of Leon-Garcia's textbook (Pearson, 2008)
,Chapter 1: Probability Models in Electrical and Computer
Engineering (Questions 1–15)
1. In the context of mathematical modeling, a deterministic model is one in which:
A. Outcomes are governed by chance
B. The future state is completely determined by initial conditions
C. Statistical regularity is the primary tool
D. Random variables are the main building blocks
Rationale: A deterministic model produces the same output for a given set of inputs
every time. There is no randomness or uncertainty in the outcome .
2. The relative frequency of an event approaches a limit as the number of trials
increases. This property is called:
A. The axiomatic approach
B. Statistical regularity
C. Deterministic behavior
D. Conditional probability
Rationale: Statistical regularity refers to the empirical observation that relative
frequencies stabilize as the number of trials grows .
3. Which of the following is NOT a component of building a probability model?
A. Defining the sample space
B. Assigning probabilities to outcomes
C. Proving the central limit theorem
D. Identifying the random experiment
Rationale: Building a probability model involves specifying the experiment, sample
space, and probability assignments. The central limit theorem is a result derived from
probability theory, not a component of model construction .
4. In a packet voice transmission system, the random experiment might involve:
A. The exact time the packet arrives
B. Whether a packet is successfully received or lost
C. The temperature of the transmission medium
D. The color of the packet header
,Rationale: Packet loss/arrival is a classic random experiment in communication systems.
The outcome is uncertain and can be modeled probabilistically .
5. A system consists of two components in series. Each component has reliability
0.9. The system reliability is:
A. 0.9
B. 0.95
C. 0.81
D. 0.99
Rationale: For series systems, reliability = product of individual reliabilities. 0.9 × 0.9 =
0.81 .
6. The axiomatic approach to probability theory requires that probabilities satisfy:
A. Only the normalization condition
B. Non-negativity, normalization, and countable additivity
C. Statistical regularity only
D. Deterministic outcomes only
Rationale: Kolmogorov's axioms: P(A) ≥ 0, P(Ω) = 1, and for disjoint events, P(∪Aᵢ) =
ΣP(Aᵢ) .
7. In reliability calculations, the failure rate function is often denoted as:
A. F(t)
B. h(t) or λ(t)
C. R(t)
D. f(t)
Rationale: The failure rate (hazard rate) function h(t) describes the instantaneous rate of
failure given survival up to time t .
8. A system with components in parallel has reliability:
A. Always less than the least reliable component
B. Always greater than or equal to the most reliable component
C. Equal to the product of component reliabilities
D. Independent of component reliabilities
Rationale: Parallel systems succeed if at least one component works, so system
reliability ≥ max(component reliabilities) .
, 9. Probability models are preferred over deterministic models when:
A. The system is perfectly predictable
B. There is inherent randomness or uncertainty in the system
C. The system has no inputs
D. The system is linear
Rationale: Probability models are appropriate when outcomes are uncertain and
statistical regularity can be observed .
10. Resource sharing systems are often analyzed using probability models because:
A. Resource demands are deterministic
B. Arrival times and service demands are random
C. Resources are infinite
D. There is no uncertainty
Rationale: In resource sharing (e.g., computer networks, telephone systems), user
arrivals and service times are inherently random .
11. The sample space of an experiment is:
A. A single outcome
B. The set of all possible outcomes
C. A subset of outcomes
D. The probability of an outcome
Rationale: The sample space Ω is the set of all possible outcomes of a random
experiment .
12. An event is defined as:
A. A single outcome
B. A subset of the sample space
C. The probability of an outcome
D. The complement of the sample space
Rationale: An event is any subset of the sample space to which a probability can be
assigned .
13. The union of events A and B (A ∪ B) represents:
