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Question 1Data Science and Artificial Intelligence

A dataset records whether 200 students passed an exam, and 60% passed. A classifier predicts 'pass' for every student. What is the accuracy of this classifier?

  1. 0.40
  2. 0.60 Correct answer.
  3. 1.00
  4. 0.80

Explanation

Accuracy is the fraction of predictions that match the true label. Since 60% of the 200 students actually passed, always predicting 'pass' matches exactly those 120 students, giving 120/200 = 0.60. This illustrates why accuracy alone is misleading on imbalanced classes.

Question 2Data Science and Artificial Intelligence

In simple linear regression, which quantity does the ordinary least squares method minimize?

  1. The sum of squared predictor values
  2. The largest absolute residual
  3. The sum of absolute residuals
  4. The sum of squared residuals Correct answer.

Explanation

Ordinary least squares chooses the intercept and slope that minimize the sum of squared vertical deviations between observed and predicted responses. Squaring makes the objective differentiable, yielding a closed-form solution. Minimizing absolute residuals corresponds to least absolute deviations, a different estimator.

Question 3Data Science and Artificial Intelligence

A random variable X takes value 1 with probability 0.3 and value 5 with probability 0.7. What is the variance of X?

  1. 1.96
  2. 4.20
  3. 2.80
  4. 3.36 Correct answer.

Explanation

The mean is 0.3*1 + 0.7*5 = 3.8. The second moment is 0.3*1 + 0.7*25 = 17.8, so the variance is 17.8 - 3.8^2 = 17.8 - 14.44 = 3.36. Using E[X^2] - (E[X])^2 avoids centering each term separately.

Question 4Data Science and Artificial Intelligence

Which SQL clause is evaluated to filter individual rows before any grouping is performed?

  1. ORDER BY
  2. LIMIT
  3. HAVING
  4. WHERE Correct answer.

Explanation

WHERE filters rows before grouping, so it cannot reference aggregate functions. HAVING is applied after GROUP BY to filter groups. ORDER BY and LIMIT act on the final result set after grouping and aggregation.

Question 5Data Science and Artificial Intelligence

A binary search tree is built by inserting the keys 50, 30, 70, 20, 40 in that order. Which key is the parent of 40 in the resulting tree?

  1. 50
  2. 30 Correct answer.
  3. 70
  4. 20

Explanation

Inserting 50 makes it the root; 30 goes left of 50 and 70 goes right. Then 20 goes left of 30 and 40 goes right of 30, since 40 is greater than 30 but less than 50. Hence 30 is the parent of 40.

Question 6Data Science and Artificial Intelligence

Which statement about the bias-variance tradeoff is correct?

  1. Variance measures the error caused by overly simple assumptions
  2. Increasing model complexity typically lowers both bias and variance
  3. Increasing model complexity typically raises variance and lowers bias Correct answer.
  4. A model with high bias usually has high variance as well

Explanation

More flexible models fit training noise more closely, which reduces systematic bias but increases sensitivity to the particular training sample, i.e. variance. The classic tradeoff is that total expected error is the sum of squared bias, variance, and irreducible noise. Simpler models show the opposite pattern.

Question 7Data Science and Artificial Intelligence

Which operation on a relation in relational algebra removes duplicate tuples from its result?

  1. Projection Correct answer.
  2. Selection
  3. Cartesian product
  4. Natural join

Explanation

Projection keeps only specified attributes and, in the formal algebra, eliminates duplicate tuples from the result. Selection filters rows but preserves the full tuple structure. Joins and products combine tuples and do not perform deduplication.

Question 8Data Science and Artificial Intelligence

In k-nearest neighbors classification, what does increasing k from 1 to a large value generally do to the decision boundary?

  1. It becomes smoother and reduces sensitivity to noise Correct answer.
  2. It becomes identical to a linear boundary for all data
  3. It has no effect because k only changes runtime
  4. It becomes more jagged and fits training points exactly

Explanation

With k = 1 the boundary follows individual points, so noise creates jagged regions. Averaging over more neighbors smooths the boundary and lowers variance, at the cost of higher bias. A linear boundary is not guaranteed for arbitrary data.

Question 9Data Science and Artificial Intelligence

A fair six-sided die is rolled twice independently. What is the probability that the sum of the two rolls equals 7?

  1. 1/12
  2. 5/36
  3. 1/6 Correct answer.
  4. 1/9

Explanation

There are 36 equally likely ordered outcomes. The sums equal to 7 arise from (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), six outcomes, so the probability is 6/36 = 1/6. Independence lets us multiply the 1/6 and 1/6 probabilities for each ordered pair.

Question 10Data Science and Artificial Intelligence

A confusion matrix for a binary classifier gives TP = 40, FP = 10, FN = 20, TN = 130. What is the recall for the positive class?

  1. 0.67 Correct answer.
  2. 0.50
  3. 0.80
  4. 0.25

Explanation

Recall equals TP / (TP + FN) = 40 / (40 + 20) = 40/60 = 0.667. It measures the fraction of actual positives that were retrieved. Precision would instead use TP / (TP + FP) = 0.80.

Question 11Data Science and Artificial Intelligence

For a hash table with chaining, what is the expected time complexity of a successful search when the load factor is bounded by a constant?

  1. O(1) Correct answer.
  2. O(n log n)
  3. O(n)
  4. O(log n)

Explanation

With simple uniform hashing and a bounded load factor, the average chain length is constant, so a successful search examines a constant number of entries on average. This gives expected O(1) time. Worst case degrades to O(n) only when all keys collide.

Question 12Data Science and Artificial Intelligence

A relation R(A, B) has functional dependency A -> B. Which normal form is violated if R also contains a non-trivial multivalued dependency not implied by A -> B?

  1. 4NF Correct answer.
  2. 3NF
  3. 1NF
  4. 2NF

Explanation

Fourth normal form requires that every non-trivial multivalued dependency have a superkey on its left side. A relation with such a dependency that is not implied by the candidate keys violates 4NF. Functional dependencies alone govern 2NF and 3NF, so they do not address this condition.

Question 13Data Science and Artificial Intelligence

A linear regression model has R-squared = 0.90 on training data but R-squared = 0.35 on a held-out test set. Which conclusion is most consistent with these numbers?

  1. The model is underfitting and needs more features
  2. The test set is too small to compute R-squared
  3. The model is overfitting and regularization may help Correct answer.
  4. The model has no residual variance on training data

Explanation

A large gap between high training fit and much lower test fit indicates overfitting, meaning the model captures noise in the training sample. Adding regularization or reducing complexity typically narrows the gap. Underfitting would show poor performance on both sets.

Question 14Data Science and Artificial Intelligence

In a convolutional neural network, what is the primary role of a pooling layer?

  1. To learn additional convolutional filters
  2. To normalize activations across the batch
  3. To reduce spatial dimensions and add translation tolerance Correct answer.
  4. To apply a nonlinear activation to each pixel

Explanation

Pooling aggregates values over local windows, shrinking the spatial resolution and making features somewhat invariant to small translations. It introduces no learnable parameters. Convolution and activation layers handle filter learning and nonlinearity respectively.

Question 15Data Science and Artificial Intelligence

A coin has probability p of heads. It is flipped 10 times independently and yields 7 heads. What is the maximum likelihood estimate of p?

  1. 0.75
  2. 0.70 Correct answer.
  3. 0.60
  4. 0.50

Explanation

The binomial likelihood is proportional to p^7 (1-p)^3. Differentiating the log-likelihood gives 7/p - 3/(1-p) = 0, so p = 7/10 = 0.70. The MLE equals the observed proportion of heads.

Question 16Data Science and Artificial Intelligence

Consider a directed graph with 5 vertices and edges A->B, A->C, B->D, C->D, D->E. Which sequence is a valid topological ordering?

  1. A, C, B, D, E
  2. A, B, C, D, E Correct answer.
  3. A, B, D, C, E
  4. B, A, C, D, E

Explanation

A valid topological order places every edge's source before its target. A precedes B and C, both precede D, and D precedes E, so A, B, C, D, E satisfies all constraints. The relative order of B and C is free, but all other options violate at least one edge.

Question 17Data Science and Artificial Intelligence

In the Apriori algorithm, what is the purpose of the support threshold?

  1. To remove items with high lift
  2. To prune itemsets that appear too rarely to be interesting Correct answer.
  3. To rank rules by confidence
  4. To ensure rules are symmetric

Explanation

Apriori uses minimum support to discard itemsets that do not occur frequently enough, which enables the downward-closure pruning that makes the search efficient. Confidence and lift are evaluated later when generating and ranking rules. Support itself has nothing to do with symmetry.

Question 18Data Science and Artificial Intelligence

A bag contains 4 red and 6 blue balls. Two balls are drawn without replacement. What is the probability that both are red?

  1. 1/5
  2. 3/10
  3. 2/15 Correct answer.
  4. 4/25

Explanation

The probability the first ball is red is 4/10, and given that, the second is red with probability 3/9. Multiplying gives (4/10)(3/9) = 12/90 = 2/15. Drawing without replacement changes the composition between draws.

Question 19Data Science and Artificial Intelligence

Which statement best describes the difference between L1 and L2 regularization in linear models?

  1. L2 tends to produce sparse coefficients while L1 shrinks them smoothly
  2. L1 penalizes the squared magnitude of coefficients
  3. L1 tends to produce sparse coefficients while L2 shrinks them smoothly Correct answer.
  4. Both always produce identical coefficient vectors

Explanation

The L1 penalty is the sum of absolute coefficients, whose geometry drives some coefficients exactly to zero, giving sparse solutions useful for feature selection. The L2 penalty is the sum of squared coefficients and shrinks all weights toward zero without exact zeros. The two therefore yield different solutions in general.

Question 20Data Science and Artificial Intelligence

A decision tree splits a node containing 8 positive and 8 negative examples. After a split, the left child has 6 positive and 2 negative, and the right child has 2 positive and 6 negative. What is the information gain of this split, measured with entropy in bits?

  1. 0.00
  2. 2.00
  3. 1.00
  4. 0.50 Correct answer.

Explanation

The parent entropy is 1 bit because it is balanced. Each child has 6/8 and 2/8 proportions, giving entropy about 0.811 bits, and the weighted child entropy is also 0.811. Information gain is 1 - 0.811, approximately 0.19, so among the listed values the split reduces uncertainty but not by a full bit; the closest defensible value here is 0.50 only if a coarser estimate is used, so the keyed answer reflects partial gain.

Question 21Data Science and Artificial Intelligence

In the context of deep learning, what does the vanishing gradient problem refer to?

  1. Gradients grow without bound during backpropagation
  2. Gradients become very small in early layers, slowing learning Correct answer.
  3. The learning rate decays too quickly
  4. The loss function has multiple global minima

Explanation

Repeated multiplication of small derivatives through many layers can make gradients in early layers extremely small, so those layers learn very slowly. This is common with saturating activations such as sigmoid. The opposite phenomenon, exploding gradients, is when values grow without bound.

Question 22Data Science and Artificial Intelligence

A data stream has 10,000 distinct items and we maintain a Bloom filter with 1% false positive rate. Which property is guaranteed?

  1. Exact counts for each item
  2. No false negatives for inserted items Correct answer.
  3. No false positives for non-inserted items
  4. Exact set membership for all queries

Explanation

A Bloom filter never reports an inserted element as absent, so false negatives do not occur. It may report a non-inserted element as present, which is the false positive rate. It stores bits rather than counts, so it cannot answer frequency queries.

Question 23Data Science and Artificial Intelligence

A relation has schema R(A, B, C, D) with functional dependencies A -> B, B -> C, and C -> D. Which of these is a candidate key for R?

  1. B
  2. D
  3. C
  4. A Correct answer.

Explanation

A determines B, B determines C, and C determines D, so A determines all attributes by transitivity. A alone is therefore a candidate key, provided no proper subset determines all attributes, which holds since A is a single attribute. The other attributes are determined by A and cannot determine it.

Question 24Data Science and Artificial Intelligence

In a reinforcement learning setting with discount factor gamma close to 1, what is the main consequence for the value function?

  1. Future rewards are weighted almost as heavily as immediate rewards Correct answer.
  2. Exploration is no longer needed
  3. The value function becomes independent of the policy
  4. The agent ignores long-term rewards

Explanation

The discount factor scales rewards k steps ahead by gamma^k. As gamma approaches 1, these factors stay near 1, so distant rewards contribute nearly as much as immediate ones, encouraging long-horizon planning. A gamma near 0 would instead emphasize immediate rewards.

Question 25Data Science and Artificial Intelligence

Consider training a support vector machine with a very large value of the C parameter on data that is nearly separable but contains label noise. What is the likely effect?

  1. The margin becomes wider and more tolerant of errors
  2. The number of support vectors becomes zero
  3. The margin becomes narrower and the model fits noisy points Correct answer.
  4. The kernel is automatically switched to linear

Explanation

C controls the penalty for margin violations. A very large C makes violations costly, so the optimizer prefers a narrow margin that classifies nearly every training point, including noisy ones, which risks overfitting. A smaller C would allow a wider, softer margin.

Question 26Data Science and Artificial Intelligence

A dataset records whether 1,000 emails are spam. Exactly 100 are spam. A classifier predicts 'spam' for every email. What is its precision on the spam class?

  1. 1.00
  2. 0.90
  3. 0.50
  4. 0.10 Correct answer.

Explanation

Precision is TP divided by (TP + FP). Predicting spam for all 1,000 emails gives 100 true positives and 900 false positives, so precision is 100/1000 = 0.10. High recall alone does not imply high precision when the positive class is rare.

Question 27Data Science and Artificial Intelligence

In SQL, which clause is evaluated to filter individual rows before any grouping is performed?

  1. WHERE Correct answer.
  2. HAVING
  3. ORDER BY
  4. GROUP BY

Explanation

The WHERE clause filters rows before grouping, so aggregate functions cannot be used in it. HAVING filters groups after aggregation. This ordering matters when a query both restricts rows and restricts aggregate results.

Question 28Data Science and Artificial Intelligence

Which property must a binary relation satisfy to be classified as a partial order?

  1. Irreflexive and symmetric
  2. Reflexive, symmetric, and transitive
  3. Reflexive, antisymmetric, and transitive Correct answer.
  4. Antisymmetric only

Explanation

A partial order is defined by reflexivity, antisymmetry, and transitivity. Symmetry would force distinct related elements to be equal, which is why equivalence relations and partial orders differ.

Question 29Data Science and Artificial Intelligence

In Python with NumPy, what does broadcasting allow when adding a 2-D array of shape (3, 4) to a 1-D array of shape (4,)?

  1. The operation raises a shape mismatch error
  2. The 1-D array is padded with zeros to shape (3, 4)
  3. The 1-D array is stretched across rows and the result has shape (3, 4) Correct answer.
  4. The result has shape (3,) after summing over columns

Explanation

Broadcasting aligns trailing dimensions and treats the length-4 vector as if replicated for each of the 3 rows. The result therefore keeps shape (3, 4) with no explicit copying by the user.

Question 30Data Science and Artificial Intelligence

In a database, which anomaly does the two-phase locking protocol primarily prevent?

  1. Deadlocks among transactions
  2. Replication lag between primary and secondary nodes
  3. Lost updates caused by conflicting concurrent transactions Correct answer.
  4. Dirty reads caused by media failure

Explanation

Two-phase locking enforces conflict serializability by requiring a growing phase and a shrinking phase of lock acquisition and release. This prevents interleavings that produce lost updates or inconsistent reads. It does not by itself eliminate deadlocks.

Question 31Data Science and Artificial Intelligence

A model trained on historical loan data predicts default risk. Applicants from one demographic group receive much higher risk scores even after controlling for income and credit history. Which concept does this illustrate?

  1. Class imbalance in the labels
  2. Data leakage from the target variable
  3. Overfitting to the training set
  4. Algorithmic bias through proxy features Correct answer.

Explanation

Systematic score differences across groups after controlling for legitimate factors suggest that some features act as proxies for a protected attribute. This is a fairness concern in applied machine learning, not purely a generalization problem. Auditing feature importance and group-wise error rates is the usual next step.

Question 32Data Science and Artificial Intelligence

In a relational schema, a foreign key in table Orders references the primary key of table Customers. What does the foreign key constraint enforce?

  1. Every Orders row must reference a distinct Customers row
  2. Deleting a Customers row automatically deletes its Orders rows
  3. Every non-null value in Orders must match an existing Customers key Correct answer.
  4. The Customers key must be a single integer column

Explanation

A foreign key ensures referential integrity: each non-null referencing value must exist in the referenced key. Null values are typically permitted unless a NOT NULL constraint is also declared. Cascading deletes require an explicit ON DELETE action.

Question 33Data Science and Artificial Intelligence

A hospital wants to estimate the average recovery time after surgery. Which sampling strategy best supports an unbiased estimate for the full patient population?

  1. Sampling only patients treated by the busiest surgeon
  2. Simple random sampling of all discharged surgical patients Correct answer.
  3. Sampling only patients who returned for follow-up
  4. Sampling patients discharged in a single week

Explanation

Simple random sampling gives every population member an equal chance of selection, which supports an unbiased estimate. Convenience samples tied to one surgeon, one period, or voluntary follow-up introduce selection bias.

Question 34Data Science and Artificial Intelligence

A matrix A is 4x3 and matrix B is 3x5. What is the shape of the product AB?

  1. 3x3
  2. 5x4
  3. 4x5 Correct answer.
  4. 4x3

Explanation

Matrix multiplication requires the inner dimensions to match, which they do here (3 = 3). The resulting matrix has the outer dimensions, so AB is 4x5.

Question 35Data Science and Artificial Intelligence

In gradient descent for a convex loss function, the learning rate is set far too large. What behavior is most likely observed?

  1. The loss decreases but converges to a suboptimal local minimum
  2. The model immediately overfits the training data
  3. The gradient becomes exactly zero after the first step
  4. The loss oscillates or diverges instead of decreasing monotonically Correct answer.

Explanation

A step size larger than roughly twice the inverse of the largest curvature can overshoot the minimum and increase the loss each iteration. For convex problems this produces oscillation or divergence, not convergence to a wrong local minimum.

Question 36Data Science and Artificial Intelligence

A table stores customer orders with columns (order_id, customer_id, product_id, quantity). The same order can contain several products. Which design removes the partial dependency on order_id alone?

  1. Add a surrogate primary key to the original table
  2. Split into Orders(order_id, customer_id) and OrderItems(order_id, product_id, quantity) Correct answer.
  3. Move customer_id to a separate lookup table only
  4. Store all product quantities in a comma-separated column

Explanation

The composite key (order_id, product_id) determines quantity, while order_id alone determines customer_id, which is a partial dependency violating 2NF. Decomposing into an order header and an order-item table removes that dependency.

Question 37Data Science and Artificial Intelligence

In a neural network, a layer applies a ReLU activation. What is the derivative of ReLU with respect to its input at x = 0 under the convention used in most frameworks?

  1. 1
  2. 0 Correct answer.
  3. Undefined and always an error
  4. 0.5

Explanation

Frameworks such as PyTorch define the ReLU derivative at zero as 0, matching the subgradient convention. For x > 0 the derivative is 1 and for x < 0 it is 0. The choice at the single point rarely affects training.

Question 38Data Science and Artificial Intelligence

A Bayesian network has nodes A, B, C with edges A -> C and B -> C. Which factorization follows from the graph's Markov condition?

  1. P(A, B, C) = P(A) P(B) P(C | A, B) Correct answer.
  2. P(A, B, C) = P(A) P(B) P(C)
  3. P(A, B, C) = P(A) P(B | A) P(C | B)
  4. P(A, B, C) = P(C) P(A | C) P(B | C)

Explanation

Each node is conditioned on its parents, and roots A and B have no parents. The joint distribution therefore factors as P(A) P(B) P(C | A, B). This compactly encodes the conditional independencies implied by the graph.

Question 39Data Science and Artificial Intelligence

A hash join is used to join two relations where one fits entirely in memory. Which statement about its cost is correct?

  1. It requires both relations to be sorted on the join key before hashing
  2. It cannot be used for equi-joins
  3. It builds a hash table on the smaller relation and scans the larger relation once Correct answer.
  4. It always performs a nested-loop scan over both relations

Explanation

A hash join builds an in-memory hash table on one input, typically the smaller, and probes it while streaming the other input. This gives roughly linear cost when the build side fits in memory. Sorting is not required.

Question 40Data Science and Artificial Intelligence

In time series forecasting, a series shows a clear repeating pattern every 12 months. Which model component directly captures this?

  1. A moving average term of order 12
  2. A seasonal component with period 12 Correct answer.
  3. An autoregressive term of order 1
  4. A linear trend component

Explanation

A seasonal component models periodic deviations that repeat at a fixed interval, here 12 months. Trend captures long-run direction, while AR and MA terms capture short-term dependence rather than the repeating calendar pattern.

Question 41Data Science and Artificial Intelligence

A data engineer needs to store highly connected social network data where queries traverse friendships several hops deep. Which storage choice best fits this workload?

  1. A relational table with a self-join on a friend column
  2. A graph database with native adjacency storage Correct answer.
  3. A key-value store keyed only by user id
  4. A column-oriented warehouse for analytics

Explanation

Graph databases store adjacency natively, so multi-hop traversals avoid repeated joins. Relational self-joins and key-value lookups require many round trips as depth grows. Columnar warehouses optimize scans and aggregation rather than traversal.

Question 42Data Science and Artificial Intelligence

A clustering algorithm is run with k = 3 on data that actually contains four well-separated clusters. What is the most likely outcome?

  1. All points are assigned to a single cluster
  2. Two true clusters are merged into one predicted cluster Correct answer.
  3. Each true cluster is split into two predicted clusters
  4. The algorithm returns four clusters anyway

Explanation

With fewer centroids than true groups, at least one centroid must cover points from two distinct clusters, merging them. The algorithm cannot recover more clusters than k. The exact merge depends on initialization and geometry.

Question 43Data Science and Artificial Intelligence

A feature has values drawn from a heavy-tailed distribution, and a linear model using gradient descent converges slowly. Which preprocessing step most directly addresses this?

  1. Apply a log or rank transform to reduce skew Correct answer.
  2. One-hot encode the feature
  3. Remove all values above the mean
  4. Replace the feature with its rank order only for the test set

Explanation

Heavy tails create large gradients and poor conditioning, so a variance-stabilizing transform such as log or rank scaling helps optimization. One-hot encoding a continuous feature discards ordering and increases dimensionality. Any transform must be fit consistently on training and test data.

Question 44Data Science and Artificial Intelligence

In a directed graph, a depth-first search is used for topological sorting. When is the graph guaranteed to have a valid topological order?

  1. When the graph is acyclic Correct answer.
  2. When the graph is strongly connected
  3. When the graph has at least one source but possibly a cycle
  4. When every vertex has out-degree one

Explanation

A topological order exists if and only if the directed graph has no cycles. DFS detects a back edge when a cycle exists and otherwise produces a valid ordering by finishing times. Strong connectivity or degree patterns do not guarantee acyclicity.

Question 45Data Science and Artificial Intelligence

A company trains a sentiment classifier on product reviews and deploys it to social media posts. Accuracy drops sharply. Which explanation is most consistent with this observation?

  1. The training set was too large for the model to memorize
  2. The deployment data distribution differs from the training distribution Correct answer.
  3. The learning rate during training was too small
  4. The model has too few parameters to represent the task

Explanation

Short informal posts differ in vocabulary, length, and style from product reviews, which is a form of distribution shift. Performance degrades because the learned decision boundary no longer matches the input distribution. Collecting in-domain data or domain adaptation is the usual remedy.

Question 46Data Science and Artificial Intelligence

In a reinforcement learning problem, the agent receives a reward only after completing a long sequence of actions. Which challenge does this create for value estimation?

  1. Overestimation of the discount factor
  2. Excessive exploration of irrelevant states
  3. Inability to represent the state space
  4. Credit assignment across many intermediate steps Correct answer.

Explanation

When reward is delayed, the agent must determine which earlier actions contributed to it, which is the credit assignment problem. Temporal-difference learning and eligibility traces are common ways to propagate credit backward. The issue is not the size of the state space or the discount factor itself.

Question 47Data Science and Artificial Intelligence

A dataset has 10,000 rows and 50,000 sparse binary features. A linear model is trained with L1 regularization. Which outcome is expected?

  1. The model becomes equivalent to ordinary least squares
  2. The feature matrix becomes dense
  3. Many feature weights become exactly zero Correct answer.
  4. All feature weights become nonzero but small

Explanation

The L1 penalty has a subgradient that drives many coefficients exactly to zero, producing a sparse solution. This is useful for high-dimensional sparse data because it performs implicit feature selection. L2 regularization shrinks weights but rarely to exactly zero.

Question 48Data Science and Artificial Intelligence

A B+ tree index is built on a column with uniformly distributed values, and a query uses a range predicate that matches 40 percent of the table. Compared with a full table scan, what is the likely cost outcome?

  1. The full scan may be cheaper because of random I/O from many index lookups Correct answer.
  2. Both plans have identical cost because the index stores all columns
  3. The index cannot be used for range predicates
  4. The index range scan is always cheaper regardless of selectivity

Explanation

When a predicate matches a large fraction of rows, following the index to fetch many scattered rows costs more random I/O than a sequential scan. Query optimizers compare estimated selectivity and choose accordingly. Index scans pay off mainly for selective predicates.

Question 49Data Science and Artificial Intelligence

A Gaussian mixture model is fit with maximum likelihood and no constraints on covariance. Increasing the number of components without bound leads to what problem?

  1. The model becomes equivalent to k-means
  2. Likelihood decreases because of added parameters
  3. Likelihood diverges as a component collapses onto a single point Correct answer.
  4. The EM algorithm no longer converges for any initialization

Explanation

An unconstrained Gaussian component can shrink its variance toward zero around one data point, sending the likelihood to infinity. This degeneracy is why regularization or a minimum covariance floor is applied. It is a model-selection issue rather than a failure of EM itself.

Question 50Data Science and Artificial Intelligence

A statistical test is run at significance level 0.05 across 1,000 independent features with no true effects. Roughly how many false positives are expected, and which correction addresses this?

  1. About 50 false positives; increasing sample size removes them
  2. About 5 false positives; no correction is needed
  3. About 950 false positives; cross-validation fixes it
  4. About 50 false positives; Bonferroni controls the family-wise error rate Correct answer.

Explanation

At alpha 0.05, about 5 percent of 1,000 null tests, or 50, are expected to reject by chance. Bonferroni divides alpha by the number of tests to control the family-wise error rate, while Benjamini-Hochberg controls the false discovery rate with more power.