A bowl contains 6 red apples and 20 green apples. What is the chance of randomly picking a red apple?

A 2x2 patch in an activation map has the following entries: [0, 4], [4, 8]. What is the result of applying an average pooling operation over this patch?

In a poll of 400 voters, 250 stated they support the new law. Calculate the 99% confidence interval for the population proportion. (Let z=2.576)

A box holds 5 red balls, 3 blue balls, and 2 green balls. If you draw two balls sequentially without putting them back, what is the likelihood that both are red?

A text file has the tokens ["swimming", "swims", "swam"]. If you use a dictionary-backed Lemmatizer (configured for verbs), how many distinct lemmas will you get?

Given that the variance of a continuous random variable Y is 16, what is its standard deviation?

Does the coordinate (1, 1) satisfy the inequality 5x + 5y <= 10?

Does the coordinate (2, 2) satisfy the inequality 2x + 3y <= 12?

When applying K-Means clustering, what usually happens if you increase K until it equals the total number of observations?

For a dataset that is heavily skewed, lacks normality, and contains many outliers, which correlation metric should be chosen, and what assumption needs checking prior to an ANOVA?

The chance of selecting a broken widget is 0.01. If a batch of 500 widgets is inspected, how many broken widgets do you expect to find?

Compute the test statistic for a single proportion test given a sample proportion of 0.55, a null proportion of 0.50, and a sample size of 100.

You convolve a 3x3 block of an image (all pixels having an intensity of 2) with a 3x3 filter consisting entirely of ones. What is the scalar output prior to any activation? (Ignore bias)

Suppose support(A) = 0.2, support(B) = 0.3, and support(A U B) = 0.1. What is the Lift for the association rule A -> B?

Compute the cosine similarity between product X (scores: [2, 2, 1]) and product Y (scores: [1, 2, 2]).

Determine the 95% confidence interval given a sample average of 50, a standard deviation of 10, and 100 observations. (Use z=1.96)

A collection has 100 files. The word "info" shows up 5 times in File X, which contains 50 words overall. The word "info" appears in exactly 10 files. Using TF = (term count) / (total words) and IDF = log10(N / df), compute the TF-IDF score for "info" in File X.

An Exponential Moving Average (EMA) uses a smoothing factor of 0.2. If the prior EMA was 50 and the newly observed value is 60, calculate the updated EMA.

Find the Euclidean distance separating coordinate A(2, 3) from coordinate B(5, 7).

In a log of 10 purchases, Product X is bought 7 times, and Product Y is bought 6 times. They are bought together 4 times. What is the support for the itemset {X, Y}?

Consider the TF-IDF vectors: vec1 = [0.6, 0.8, 0] and vec2 = [0.3, 0.4, 0]. Calculate the cosine similarity between vec1 and vec2.

In a K-Means algorithm, two data points A(2,2) and B(4,4) are assigned to the same cluster. Where is their centroid located?

When analyzing clusters, if a subset of instances is segregated into an "Anomalies" cluster, how should you interpret this group?

Compute the local clustering coefficient for a vertex connected to 3 other vertices, assuming those connected vertices share exactly 1 edge among themselves.

What is the defining characteristic of a Stationary time series?

Find the cosine similarity between client A with profile [1, 2] and client B with profile [2, 4].

An Augmented Dickey-Fuller (ADF) test on a dataset yields a p-value of 0.02. Using an alpha level of 0.05, what is the appropriate interpretation?

In a small web graph (Page 1 links to 2 and 3; Page 2 links to 3; Page 3 links to 1) with an initial PageRank of 1/3 for each, what is the PageRank of Page 2 after one update step?

A dataset of 25 measurements yields a mean of 120 and a standard deviation of 15. Determine the 90% confidence interval for the true mean. (t-value for df=24 is 1.711)

Does the origin (0, 0) satisfy the linear constraint 3x + 4y >= 12?

What term describes the phenomenon where similar entities in a graph tend to form connections with one another?

In Recommendation Engines, what is the main goal of content-based filtering?

Which challenge is frequently encountered by collaborative filtering techniques when introducing fresh products to the catalog?

To identify the correct order for a Moving Average (MA) model, which visualization helps pinpoint the appropriate lag 'q'?

A drawer contains 2 rigged coins (75% probability of heads) and 3 normal coins (50% probability of heads). You blindly pick one and flip it, getting heads. What is the chance that you picked a rigged coin?

Suppose a quiz has 5 questions, each offering 4 choices. What is the chance of guessing exactly 3 of them right?

When analyzing digital pictures, what is the main difference between color (RGB) and monochrome (grayscale) formats?

Compute the Within-Cluster Sum of Squares (WCSS) for a cluster that has instances at (1,1) and (1,3) with its center at (1,2).

A network of 5 individuals has an average shortest path length of 2.5. What is the total sum of the shortest paths across all unique pairs of individuals?

Why do standard Convolutional Neural Networks (CNNs) struggle when applied directly to graph structures?

The leverage metric for an association rule A -> B is support(A U B) - (support(A) * support(B)). If A has support 0.4, B has support 0.5, and A U B has support 0.25, calculate the leverage.

Consider the chronological sequence: 10, 20, 30, 40, 50. Calculate the Simple Moving Average (SMA) for the final period using a 3-period window.

Find the cosine similarity between reviewer X (ratings: [3, 4]) and reviewer Y (ratings: [4, 3]).

A dataset contains 5 sequences: {M, O, N, K, E, Y}, {D, O, N, K, E, Y}, {M, A, K, E}, {M, U, C, K}, {C, O, O, K, I, E}. Compute the support for element 'K'.

Given true targets [10, 20] and model outputs [12, 16], calculate the Mean Squared Error (MSE).

Calculate the total number of trainable weights (including biases) in a 2D convolution layer that has 8 filters of size 3x3 and processes an input volume with 3 channels.

In collaborative filtering, what is the role of the Pearson correlation coefficient?

The association rule {Chips, Salsa} -> {Guacamole} boasts an 80% confidence, and the itemset {Chips, Salsa} appears in 25% of transactions. What is the support for {Chips, Salsa, Guacamole}?

Calculate the value of the function Z = 5x + 2y at the coordinates (4, 1).

What primarily distinguishes Stemming from Lemmatization?