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[QZ] 3

Tags: #◇CSMODEL #◇Mock Exams #◇Computer Science #◇Data Science #◇Statistical Modeling #◇Python #◇Machine Learning


Mock Exam 3

◇Overview

This third mock examination assesses mastery of probability models, information retrieval, NLP preprocessing (stemming vs. lemmatization), association rule mining, and optimization functions.

◇References & Navigation

CONFIRMATION // 理解度の確認

ACTIVE RECALL VERIFICATION

Select an answer to verify conceptual comprehension and reveal the technical rationale.

Q1

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

Q2

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?

Q3

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)

Q4

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?

Q5

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?

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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?

Q11

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?

Q12

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.

Q13

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)

Q14

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?

Q15

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

Q16

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

Q17

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.

Q18

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.

Q19

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

Q20

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}?

Q21

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.

Q22

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?

Q23

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

Q24

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

Q25

What is the defining characteristic of a Stationary time series?

Q26

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

Q27

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?

Q28

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?

Q29

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)

Q30

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

Q31

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

Q32

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

Q33

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

Q34

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

Q35

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?

Q36

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

Q37

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

Q38

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).

Q39

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?

Q40

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

Q41

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.

Q42

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

Q43

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

Q44

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'.

Q45

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

Q46

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.

Q47

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

Q48

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}?

Q49

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

Q50

What primarily distinguishes Stemming from Lemmatization?

[QZ] 3 | PROJECT ENGRAM