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CS 7638 MIDTERM PRACTICE EXAM 2026 ALL
QUESTIONS AND CORRECT DETAILED
ANSWERS ALREADY A GRADED |NEW AND
REVISED
A robot correctly follows a movement request with a probability of 0.9.
Otherwise, it will stay in current location with a probability of 0.1.
Assuming a cyclical world, what is the probability of the 3-cell grid,
after ONE movement to the left?
Cell [probability]: 1 [0.3] | 2 [0.4] | 3 [0.2] - ANSWER- 1 [0.39] | 2
[0.22] | 3 [0.29]
Limit distribution - ANSWER- The location probabilities in a robot's
grid cell become uniform if you move the robot infinite times with
inaccurate robot motion.
Localization summary - ANSWER- Belief is a probability of the robot's
location. Sensing is a product with normalization. Movement is a
convolution (aka addition) using the total probability theorem.
Q: Which probability theorem or rule does a measurement/sense use? -
ANSWER- Bayes' Theorem
Q: Which probability theorem or rule does movement use? - ANSWER-
The Total Probability Rule
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Bayes' Theorem - ANSWER- A method used to compute posterior
probabilities. Measurement or sense functions use this theorem. The
denominator in the image can also be written as P(B).
Total Probability Rule or Law of Probability - ANSWER- P(A) = P(A l
B₁)(P(B₁) + P(A l B₂)P(B₂) +....P(A l Bn)P(Bn). The unconditional
probability of event, given conditional probabilities. Movement
functions use this.
Histogram Filters - ANSWER- A discrete filter that's also multimodal (it
can have multiple Gaussian peaks in its line of belief). They have
exponential space complexity.
Kalman Filters - ANSWER- A continuous filter used to estimate an
object's velocity. It's only unimodal, and it has quadratic space
complexity.
Gaussian distribution formula - ANSWER- Sigma is standard deviation.
Sigma squared is variance.
Mu is the mean.
X is the point or measurement we are evaluating.
Q: What is another name for variance or sigma squared? - ANSWER-
Uncertainty. The larger it is, the wider the Gaussian distribution.
CS 7638 MIDTERM PRACTICE EXAM 2026 ALL
QUESTIONS AND CORRECT DETAILED
ANSWERS ALREADY A GRADED |NEW AND
REVISED
A robot correctly follows a movement request with a probability of 0.9.
Otherwise, it will stay in current location with a probability of 0.1.
Assuming a cyclical world, what is the probability of the 3-cell grid,
after ONE movement to the left?
Cell [probability]: 1 [0.3] | 2 [0.4] | 3 [0.2] - ANSWER- 1 [0.39] | 2
[0.22] | 3 [0.29]
Limit distribution - ANSWER- The location probabilities in a robot's
grid cell become uniform if you move the robot infinite times with
inaccurate robot motion.
Localization summary - ANSWER- Belief is a probability of the robot's
location. Sensing is a product with normalization. Movement is a
convolution (aka addition) using the total probability theorem.
Q: Which probability theorem or rule does a measurement/sense use? -
ANSWER- Bayes' Theorem
Q: Which probability theorem or rule does movement use? - ANSWER-
The Total Probability Rule
, 2|Page
Bayes' Theorem - ANSWER- A method used to compute posterior
probabilities. Measurement or sense functions use this theorem. The
denominator in the image can also be written as P(B).
Total Probability Rule or Law of Probability - ANSWER- P(A) = P(A l
B₁)(P(B₁) + P(A l B₂)P(B₂) +....P(A l Bn)P(Bn). The unconditional
probability of event, given conditional probabilities. Movement
functions use this.
Histogram Filters - ANSWER- A discrete filter that's also multimodal (it
can have multiple Gaussian peaks in its line of belief). They have
exponential space complexity.
Kalman Filters - ANSWER- A continuous filter used to estimate an
object's velocity. It's only unimodal, and it has quadratic space
complexity.
Gaussian distribution formula - ANSWER- Sigma is standard deviation.
Sigma squared is variance.
Mu is the mean.
X is the point or measurement we are evaluating.
Q: What is another name for variance or sigma squared? - ANSWER-
Uncertainty. The larger it is, the wider the Gaussian distribution.
