OCA-510 MJ — Model Answers and Marking Guide

Q1 answer key

Award 1 mark for the option and 1 mark for a valid reason.

No.	Answer	Reason and closest-distractor check	Module
1	B	Rationality is defined against expected performance, not program size or sensor count.	1
2	A	PEAS specifies task performance, environment, actuators, and sensors; “actions/state” is not the expansion.	1
3	A	Sensors reveal all relevant state; observability does not imply deterministic transitions.	1
4	A	Stochastic means actions may have uncertain outcomes; it is independent of observability.	1
5	A	Internal state represents unobserved aspects/history; a simple reflex agent lacks it.	1
6	B	Actuators affect the world while sensors perceive it.	1
7	B	FIFO ordering expands by increasing depth; a LIFO stack produces DFS.	2
8	B	UCS prioritises accumulated path cost, not depth or estimated remaining cost.	2
9	A	A* combines cost so far and heuristic remaining cost; greedy uses only h.	2
10	B	Admissibility means h(n) is never above the true remaining cost; zero is allowed.	2
11	B	Safe cutoffs skip nodes that cannot affect the minimax decision; the value is unchanged.	2
12	A	Constraints restrict combinations of domain values; rewards belong to decision problems.	2
13	A	Propositional atoms have no internal object/quantifier structure.	3
14	B	FOL adds predicates, variables, functions, and quantifiers; connectives already exist in propositional logic.	3
15	B	From P and P→Q, modus ponens yields Q; Q→P is the converse.	3
16	A	Resolution combines complementary literals in clauses; probabilities are outside logical resolution.	3
17	A	Entities/concepts are nodes connected by labelled relations; a frame is attribute-slot oriented.	3
18	B	Backward chaining starts at a query and seeks rules/facts that support it.	3
19	A	Bayes combines a prior with evidence likelihood and normalisation to obtain a posterior.	4
20	A	Product factorisation characterises independence; independent events need not have equal probability.	4
21	A	A BN factorises a joint distribution with a DAG and local conditional probability tables.	4
22	A	The “naive” assumption is feature conditional independence once the class is known.	4
23	A	An HMM transitions among hidden states that probabilistically emit observations.	4
24	A	Expected utility weights each outcome's utility by probability; best-case choice ignores risk.	4
25	A	A neuron forms w·x+b and applies an activation; it is not a search operator.	5
26	A	ReLU passes positive x and returns zero for negative x; the sigmoid is option B.	5
27	C	XOR is not linearly separable, unlike AND, OR, and NOT.	5
28	A	Backpropagation propagates derivatives through layers using the chain rule.	5
29	A	Subtracting a learning-rate-scaled gradient locally reduces loss; adding it performs ascent.	5
30	A	Softmax produces nonnegative outputs summing to one across classes.	5

Q2 model answers

1. A rational agent chooses the action expected to perform best from its percepts and knowledge. Omniscience would require knowing actual future outcomes, which rationality does not assume. Marks: rationality 1; distinction 1. (Module 1)
2. A search problem specifies an initial state, actions/transition model, goal test, and path-cost function. Its solution is an action path from the initial state to a goal. Marks: components 1; solution 1. (Module 2)
3. Greedy best-first selects smallest h(n) and ignores cost already paid. A* selects smallest g(n)+h(n) and, with suitable conditions, is complete and optimal. Marks: each rule 1. (Module 2)
4. MRV chooses the unassigned variable with the fewest legal remaining values. Forward checking removes newly inconsistent values from neighbouring domains after an assignment. Marks: each method 1. (Module 2)
5. A semantic network represents concepts as nodes and relations as labelled edges. A frame represents an entity or situation with named slots, values, defaults, and inheritance. Marks: each representation 1. (Module 3)
6. X and Y are conditionally independent given Z when P(X,Y|Z)=P(X|Z)P(Y|Z). A Bayesian network encodes such independences through its graph. Marks: definition 1; graph link 1. (Module 4)
7. For error e=t−y, update w←w+ηex and b←b+ηe. Correctly classified examples have zero error and no update. Marks: weight rule 1; bias/consequence 1. (Module 5)

Q3 model answers

1. BFS uses shallowest/FIFO and is complete, and optimal for equal costs; DFS uses deepest/LIFO and is neither generally complete on infinite spaces nor optimal. UCS uses lowest g and is complete/optimal for positive bounded costs. Greedy uses lowest h and is generally neither. A* uses g+h and is complete/optimal with an admissible/consistent heuristic under standard assumptions. Rubric: BFS 1; DFS 1; UCS 1; greedy 1; A* 1. (Module 2)
2. Convert P→Q to ¬P∨Q; the other clauses are P and ¬Q. Resolve ¬P∨Q with P to obtain Q. Resolve Q with ¬Q to obtain the empty clause, a contradiction. Therefore P→Q and P entail Q. Rubric: conversion 1; clauses 1; first resolution 1; empty clause 1; conclusion 1. (Module 3)
3. P(+)=0.90(0.01)+0.05(0.99)=0.0585. Bayes gives P(D|+)=0.90×0.01/0.0585=0.153846…, about 15.38%. The modest posterior despite good sensitivity is caused by the low prior and false positives. Rubric: formula 1; numerator 1; denominator 1; result 1; interpretation 1. (Module 4)
4. Net input is 0.2(1)+(−0.1)(0)−0.3=−0.1, so output y is 0. Error is t−y=1. Update: w₁=0.2+0.1(1)(1)=0.3, w₂=−0.1+0.1(1)(0)=−0.1, and b=−0.3+0.1(1)=−0.2. Rubric: net 1; output/error 1; weights 2; bias 1. (Module 5)