Suppose we have a time sequence [10, 12, 15, 19, 24]. Calculate the second-order difference at the 5th step (the value 24).

When reviewing an Elbow curve in K-Means to find the best k, what causes the sum of squared distances to drop as k grows?

Compute the scalar product of the vector for a movie [5, 5, 5] and a user's preference vector [1, 1, 1].

In a clustering task, the centers are at C1(0, 0) and C2(10, 10). A new observation is at (3, 4). Which center will it be allocated to based on straight-line distance?

Imagine a basic PageRank setup (no damping). Website A points to B and C. Website B points to C. Website C points to A. All start with a score of 1/3. What is C's score after a single step?

Calculate the scalar product of an article's vector [0, 2, 4] and a reader's vector [3, 1, 0].

Out of 1000 store receipts, the association rule X -> Y has 15% support and 60% confidence. How many receipts include both item X and item Y?

For the same network (A points to B, C; B points to C; C points to A) with starting PR=1/3, find A's PR after one step.

A model for seasonal forecasting is written as SARIMA(1, 0, 1)(0, 1, 1)[12]. What is the order of seasonal differencing (D)?

How many subjects do we need to survey to guess a true average with a margin of error of 2 and 95% confidence, assuming the standard deviation is 15? (Use z=1.96)

Determine the storage size (in bytes) needed for an uncompressed 100x100 RGB photograph, given 8 bits (1 byte) for each color channel per pixel.

In a one-way network, Node A connects to B, C, and D. Meanwhile, C and D connect back to A. What are A's in-degree and out-degree respectively?

Calculate the value of Z = 3x + 4y at the coordinates (2, 3).

A network contains 6 vertices. If you sum all the values in its adjacency matrix, you get 14. How many connections exist in this undirected network?

Based on our class discussion, what does Principal Component Analysis (PCA) actually do when given variables like cost, rating, and duration?

A text collection has 500 files, and the term "the" shows up in every single one. What is its standard IDF value if computed using log base 10 (log10(N/df))?

Calculate the value of Z = 2x + 9y at the coordinates (3, 1).

What is the dot product of a product vector [2, 3, 1] and a customer vector [1, 2, 3]?

An image grid of size 10x10 goes through Max Pooling with a 2x2 area and a jump step of 2. What are the dimensions of the resulting grid?

Which of these is NOT an underlying assumption for conducting an independent two-sample t-test?

For a two-sided hypothesis test with a significance level of 0.05, what is the boundary z-score?

Suppose our dataset is: Doc1 = "hello world", Doc2 = "hello". Using Bag of Words, what is the one-hot representation for "world" if the words are sorted alphabetically?

In a neural network, the first convolution uses a 3x3 filter (stride 1). The second uses another 3x3 filter (stride 1). How large is the receptive field of a neuron in the second layer relative to the initial image?

Node A has 4 mutual acquaintances. There are 3 links between these 4 acquaintances. What is Node A's local clustering coefficient?

What is the main goal of using the Apriori technique in data analysis?

Compute the Lift for the rule {X} -> {Y} given (Total=10, Supp(X)=0.7, Supp(Y)=0.6, Supp(X,Y)=0.4).

What principle asserts that if a linear programming problem has an optimal result, it will be found at a corner of the valid region?

In hierarchical clustering (agglomerative), which metric uses the smallest gap between any point in one cluster and any point in another?

Which method in agglomerative clustering computes the distance between clusters by averaging the distances of all pairs of their points?

Why is it problematic to apply fit_transform() on validation/test sets during text categorization?

A sentence has the terms ["running", "runs", "ran"]. If processed by a standard Porter Stemmer, how many distinct tokens will likely remain?

Consider an AR(1) equation: y_t = 5 + 0.6 * y_{t-1}. If the previous value y_{t-1} was 10, predict y_t (with zero error).

Assuming all other factors are unchanged, what occurs to the width of a confidence interval when you increase the sample size?

Which scenario describes a Type I error?

Compute the objective function Z = x + y given the coordinates (5, 5).

Compute the objective function Z = 10x + 15y given the coordinates (1, 2).

A network with 3 vertices (X, Y, Z) contains the links (X,Y) and (X,Z). What is the trace of its corresponding adjacency matrix?

To decide the lag parameter 'p' for an Autoregressive (AR) model, which chart is mostly utilized to spot the significant cut-off point?

A chi-square goodness-of-fit analysis involves 5 distinct groups. How many degrees of freedom does it have?

A collection of numbers is at x = {2, 4, 10, 12, 3, 20, 30, 11, 25}. Using k-means (k=2) with initial centers at c1=3 and c2=4, what will the updated center c1 be after one step?

What is the core reason for adding a pooling layer in a CNN architecture?

If you use CountVectorizer(ngram_range=(1, 2)) on the text "data science is fun", how many distinct terms/phrases are extracted?

What is a recognized disadvantage of the K-Means algorithm?

In the aforementioned database, calculate the support for the combination {O, K}.

Two distinct groups provided these measurements: n1=30, mean1=50, sd1=10; n2=40, mean2=45, sd2=12. Calculate the 95% confidence interval for their mean difference. (Use z=1.96)

Given a sequence [12, 15, 14, 18, 20], compute the first-order difference at time step 4 (the value 18).

A virus is present in 1% of people. The testing kit has 99% accuracy (for both positives and negatives). If someone gets a positive result, what is the chance they truly have the virus?

Check if the coordinate (5, 0) satisfies the boundary condition 2x + y <= 8.

About 30% of messages are junk. A junk filter intercepts 95% of junk messages but also mistakenly flags 2% of normal messages as junk. If a message is flagged, what is the probability it is genuinely junk?

Calculate the value of Z = 7x + 8y given the coordinates (2, 2).