Cs 7638 Midterm Actual Exam Prep 2026 All Questions And Correct Detailed Answers With Rationales Already A Graded With Expert Feedback |New And Revised|Currently Testing

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CS 7638 MIDTERM ACTUAL EXAM PREP 2026
ALL QUESTIONS AND CORRECT DETAILED
ANSWERS WITH RATIONALES ALREADY A
GRADED WITH EXPERT FEEDBACK |NEW AND
REVISED|CURRENTLY TESTING



SECTION 1: PROBABILISTIC FOUNDATIONS, BAYES
FILTERS, AND LOCALIZATION (Questions 1–50)
1. In the context of robotics and AI 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 the inherent noise in sensors (e.g., camera, LIDAR) and
the unpredictability of actuators (e.g., wheel slippage). The real world
is uncertain, and probabilistic methods provide a mathematical
framework to manage this uncertainty.
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

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related to the event. This inverse probability relationship is essential
for robot localization and state estimation.
3. 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 variance of the sensor noise
Rationale: The "belief" is a posterior probability distribution over
possible states (e.g., poses) conditioned on all previous measurements
and control actions. It represents what the robot knows about its state
given the history of data.
4. 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 two-step
cycle: the prediction step (using the motion model) to determine the
prior, and the correction step (using the observation model) to
compute the posterior.
5. 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

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Rationale: The Markov assumption states that given the current state,
past states and observations are conditionally independent. This means
the current state captures all relevant information needed to predict
the future.
6. Why is the normalization step crucial in the Bayes filter?
A) The belief integrates to 1
B) The belief integrates to 1
C) The motion model is valid
D) The state space remains discrete
Rationale: Normalization scales the product of the prior and
likelihood so the total probability sums to 1. This ensures the output is
a proper probability distribution.
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 exact posterior distribution. It is the optimal probabilistic
estimator given the available information.
8. In a histogram filter, the state space is represented as:
A) Continuous Gaussian distributions
B) A set of discrete bins with probability masses
C) A single point estimate
D) A neural network
Rationale: Histogram filters (also known as discrete Bayes filters)
approximate continuous state spaces using a grid of discrete regions
(bins), each assigned a probability value.

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9. Which of the following properties best characterize a Histogram
Filter?
A) Continuous, Multimodal, Approximate
B) Continuous, Unimodal, Exact
C) Discrete, Multimodal, Approximate
D) Continuous, Multimodal, Exact
Rationale: Histogram filters discretize the state space, making them
discrete. They are capable of representing multimodal distributions
(multiple hypotheses) but are inherently approximate due to their
discrete nature.
10. What happens to the time and space complexity of a histogram filter
as the number of dimensions in the state space (m) increases?
A) Linear growth, O(m)
B) Quadratic growth, O(m²)
C) Exponential growth, O(n^m), where n is the resolution of the
bins
D) Logarithmic growth, O(log n)
Rationale: Histogram filters suffer from the "curse of
dimensionality." Representing an m-dimensional space with n bins per
dimension results in a grid with n^m cells, leading to exponential
growth in complexity.
11. You are modeling a robot's motion. If the 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 outcome of the motion
C) The sensors are very noisy
D) The environment is static
Rationale: In probabilistic robotics, variance is a measure of
uncertainty. A high variance in the control (motion) model indicates