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CS-7638 FINAL ACTUAL EXAM PREP 2026
ALL QUESTIONS AND CORRECT
DETAILED ANSWERS WITH RATIONALES
ALREADY A GRADED WITH EXPERT
FEEDBACK |NEW AND REVISED
Section 1: Questions 1–50 (Probabilistic Inference, Bayes Filters,
Kalman Filters)
1. In the context of robotics as taught in CS-7638, what is the primary
purpose of using probabilistic inference?
A) To ensure deterministic outcomes from robot actions
B) To handle uncertainty in sensing and action
C) To simplify the mathematical models of motion
D) To reduce the need for complex programming
*Rationale: Probabilistic inference is fundamental to robotics for
dealing with inherent noise in sensors and unpredictability of
actuators. The real world is uncertain, and probabilistic methods
provide a mathematical framework to manage this uncertainty
(source: CS-7638 exam review notes).*
2. Which formula correctly represents Bayes’ Rule?
A) P(A|B) = P(B|A) / P(A)
B) P(A|B) = P(B|A) × P(B) / P(A)
C) P(A|B) = P(B|A) × P(A) / P(B)
D) P(A|B) = P(A|B) × P(B)
Rationale: Bayes’ Rule is P(A|B) = P(B|A)·P(A)/P(B). It
describes the probability of an event based on prior knowledge of
conditions related to the event. This relationship is essential for
robot localization and state estimation.
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3. In a Bayes filter, the belief distribution bel(x_t) is typically
updated using which two steps?
A) Prediction and correction
B) Smoothing and filtering
C) Sampling and resampling
D) Detection and tracking
Rationale: Bayes filters recursively update the belief using a
prediction step (motion model) and a correction step (observation
model). The prediction step propagates the state forward, and the
correction step incorporates new measurements.
4. Which of the following best describes the Markov assumption in
Bayes filters?
A) Future states depend on all past states equally
B) Current state depends only on the immediate previous state
and current observation
C) Observations are independent of the state
D) The state space must be discrete
Rationale: The Markov assumption states that given the current
state, past states and observations are conditionally independent.
This means the future depends only on the present, not the entire
history.
5. In a robot localization problem, what does the “belief” represent?
A) The robot’s confidence in its hardware integrity
B) The robot’s probabilistic knowledge of its state (e.g.,
position) given all past data
C) The robot’s desired goal position
D) The robot’s internal clock state
Rationale: The belief is the posterior probability distribution over
the robot‘s state (usually its pose) conditioned on all previous
sensor measurements and control commands.
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6. If a control command has a high variance, what does this imply?
A) The robot is very accurate in its movement
B) There is a high level of uncertainty in the motion model
C) The sensor readings are highly reliable
D) The Kalman gain will be close to zero
Rationale: High variance in the motion model indicates low
confidence in the control command, meaning the robot’s actual
movement may deviate significantly from the commanded
motion.
7. Which statement about the Bayes filter is TRUE?
A) It requires the state space to be discrete and finite
B) It provides the optimal probabilistic estimate given
available information
C) It cannot handle non-linear observation models
D) It assumes all noise is Gaussian
Rationale: Under the Markov assumption, the Bayes filter
recursively computes the optimal posterior distribution. It can
handle non-linear models (via approximations like EKF/UKF)
and non-Gaussian noise (via particle filters).
8. What is the purpose of normalization in a Bayes filter?
A) To ensure that the motion model is valid
B) To ensure that the observation model is linear
C) To scale the product of prior and likelihood so the total
probability sums to 1
D) To reduce the computational complexity of the filter
Rationale: Normalization forces the sum of all probability
masses (or integral of the PDF) to 1, which is required for a valid
probability distribution.
9. Which assumption is fundamental to the standard (linear) Kalman
filter?
A) Non-linear motion and measurement models
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B) Gaussian noise and linear models
C) Discrete state spaces only
D) No process noise allowed
Rationale: The Kalman filter assumes that both the motion and
observation models are linear and that all noises (process and
measurement) are zero-mean Gaussian. These assumptions allow
the filter to maintain a Gaussian belief.
10. Kalman Filters are unimodal. (True/False)
A) True
B) False
Rationale: The Kalman filter maintains a single Gaussian
distribution (mean and covariance) to represent the belief. This
unimodal representation is a key limitation when dealing with
ambiguous or multi-hypothesis states.
11. Kalman Filters have exponential complexity. (True/False)
A) True
B) False
Rationale: The standard Kalman filter has polynomial
complexity (O(k³) where k is the state dimension). It does not
scale exponentially, though the complexity grows with the
square/cube of the state size.
12. What does the covariance matrix P represent in a Kalman
filter?
A) The estimated state (position and velocity)
B) The uncertainty in the state estimate
C) The mapping from control to state
D) The mapping from state to measurement
Rationale: The covariance matrix P represents the estimated
accuracy (uncertainty) of the state estimate. The diagonal
elements are the variances for each state dimension.
CS-7638 FINAL ACTUAL EXAM PREP 2026
ALL QUESTIONS AND CORRECT
DETAILED ANSWERS WITH RATIONALES
ALREADY A GRADED WITH EXPERT
FEEDBACK |NEW AND REVISED
Section 1: Questions 1–50 (Probabilistic Inference, Bayes Filters,
Kalman Filters)
1. In the context of robotics as taught in CS-7638, what is the primary
purpose of using probabilistic inference?
A) To ensure deterministic outcomes from robot actions
B) To handle uncertainty in sensing and action
C) To simplify the mathematical models of motion
D) To reduce the need for complex programming
*Rationale: Probabilistic inference is fundamental to robotics for
dealing with inherent noise in sensors and unpredictability of
actuators. The real world is uncertain, and probabilistic methods
provide a mathematical framework to manage this uncertainty
(source: CS-7638 exam review notes).*
2. Which formula correctly represents Bayes’ Rule?
A) P(A|B) = P(B|A) / P(A)
B) P(A|B) = P(B|A) × P(B) / P(A)
C) P(A|B) = P(B|A) × P(A) / P(B)
D) P(A|B) = P(A|B) × P(B)
Rationale: Bayes’ Rule is P(A|B) = P(B|A)·P(A)/P(B). It
describes the probability of an event based on prior knowledge of
conditions related to the event. This relationship is essential for
robot localization and state estimation.
,2|Page
3. In a Bayes filter, the belief distribution bel(x_t) is typically
updated using which two steps?
A) Prediction and correction
B) Smoothing and filtering
C) Sampling and resampling
D) Detection and tracking
Rationale: Bayes filters recursively update the belief using a
prediction step (motion model) and a correction step (observation
model). The prediction step propagates the state forward, and the
correction step incorporates new measurements.
4. Which of the following best describes the Markov assumption in
Bayes filters?
A) Future states depend on all past states equally
B) Current state depends only on the immediate previous state
and current observation
C) Observations are independent of the state
D) The state space must be discrete
Rationale: The Markov assumption states that given the current
state, past states and observations are conditionally independent.
This means the future depends only on the present, not the entire
history.
5. In a robot localization problem, what does the “belief” represent?
A) The robot’s confidence in its hardware integrity
B) The robot’s probabilistic knowledge of its state (e.g.,
position) given all past data
C) The robot’s desired goal position
D) The robot’s internal clock state
Rationale: The belief is the posterior probability distribution over
the robot‘s state (usually its pose) conditioned on all previous
sensor measurements and control commands.
,3|Page
6. If a control command has a high variance, what does this imply?
A) The robot is very accurate in its movement
B) There is a high level of uncertainty in the motion model
C) The sensor readings are highly reliable
D) The Kalman gain will be close to zero
Rationale: High variance in the motion model indicates low
confidence in the control command, meaning the robot’s actual
movement may deviate significantly from the commanded
motion.
7. Which statement about the Bayes filter is TRUE?
A) It requires the state space to be discrete and finite
B) It provides the optimal probabilistic estimate given
available information
C) It cannot handle non-linear observation models
D) It assumes all noise is Gaussian
Rationale: Under the Markov assumption, the Bayes filter
recursively computes the optimal posterior distribution. It can
handle non-linear models (via approximations like EKF/UKF)
and non-Gaussian noise (via particle filters).
8. What is the purpose of normalization in a Bayes filter?
A) To ensure that the motion model is valid
B) To ensure that the observation model is linear
C) To scale the product of prior and likelihood so the total
probability sums to 1
D) To reduce the computational complexity of the filter
Rationale: Normalization forces the sum of all probability
masses (or integral of the PDF) to 1, which is required for a valid
probability distribution.
9. Which assumption is fundamental to the standard (linear) Kalman
filter?
A) Non-linear motion and measurement models
, 4|Page
B) Gaussian noise and linear models
C) Discrete state spaces only
D) No process noise allowed
Rationale: The Kalman filter assumes that both the motion and
observation models are linear and that all noises (process and
measurement) are zero-mean Gaussian. These assumptions allow
the filter to maintain a Gaussian belief.
10. Kalman Filters are unimodal. (True/False)
A) True
B) False
Rationale: The Kalman filter maintains a single Gaussian
distribution (mean and covariance) to represent the belief. This
unimodal representation is a key limitation when dealing with
ambiguous or multi-hypothesis states.
11. Kalman Filters have exponential complexity. (True/False)
A) True
B) False
Rationale: The standard Kalman filter has polynomial
complexity (O(k³) where k is the state dimension). It does not
scale exponentially, though the complexity grows with the
square/cube of the state size.
12. What does the covariance matrix P represent in a Kalman
filter?
A) The estimated state (position and velocity)
B) The uncertainty in the state estimate
C) The mapping from control to state
D) The mapping from state to measurement
Rationale: The covariance matrix P represents the estimated
accuracy (uncertainty) of the state estimate. The diagonal
elements are the variances for each state dimension.
