LaTeX is a high-quality typesetting system widely used in academia, particularly in scientific publishing.

Statement i: Correct. LaTeX is widely used to prepare manuscripts for scientific journals, theses, and technical reports.

Statement ii: Correct. LaTeX is a markup language (similar to HTML in concept) that compiles into formatted PDFs/documents.

Statement iii: Correct. LaTeX is a standard for publishing scientific papers due to its ability to handle complex mathematical equations, references, and formatting.

Thus, all three statements are true → Option B (i, ii, iii).

In the Hub and Spoke analytics architecture:

The hub is the central data platform (data lake, warehouse, or unified data hub).

The spokes are the analytic use cases or applications that leverage this data to create business value.

These spokes typically help the organization:

Optimize key business processes (Option A).

Deliver improved customer experiences (Option B).

Uncover monetization opportunities (Option C).

Since all three are valid, the correct answer is Option E (All of the above).

JSON (JavaScript Object Notation) is a lightweight data-interchange format widely used for storing and exchanging structured or semi-structured data. JSON allows hierarchical (tree-like) structures, such as nested objects and arrays, to be serialized into a textual representation.

Option A (Plain text format): Correct. JSON files are stored as plain text, making them human-readable and language-independent.

Option B (Plain string format): Correct. JSON objects are transmitted as strings across networks (e.g., via APIs, RESTful services).

Option C: Incorrect. JSON does not serialize into “any format,” but specifically into text/string-based formats.

Option D: Correct. Since JSON is both plain text and transmitted as string format, the right answer is both A and B.

Option E: Incorrect.

Thus, JSON serializes hierarchical data into plain text and string formats.

A Markov chain is a stochastic process describing a sequence of possible events, where the probability of each event depends only on the state attained in the previous step (the Markov property).

Option A: Incorrect. The variables are random, not fixed.

Option B: Correct. Markov chains represent the state of a system at sequential time points.

Option C: Correct. A Markov chain is indeed a sequence of random variables {X1, X2, …} that satisfy the Markov property.

Option D: Incorrect, since A is wrong.

Option E: Correct, because both B and C are valid.

Thus, the correct answer is Option E (Both B and C).

The correct answer isPyMC(Option B).

PyMC is an open-source Python library widely used forBayesian statistical modelingandprobabilistic machine learning. It provides a robust framework for defining and fitting Bayesian networks to real data usingMarkov Chain Monte Carlo (MCMC)sampling techniques, as well asvariational inferencemethods. This makes it a powerful tool for data scientists who want to work withuncertainty modeling,probabilistic inference, andcausal reasoningin complex datasets.

Let’s clarify the other options to avoid confusion:

Option A: SciLib– There is no standard Python library by this name that is related to Bayesian networks. (It may be confused withSciPyorSciKit-Learn, but those are not specialized for Bayesian inference.)

Option C: MyLib– This is not a recognized Python package in the data science ecosystem.

Option D: MCMC– While Markov Chain Monte Carlo is thetechniqueused in Bayesian estimation, it is not a standalone library. Instead, PyMC implements MCMC as part of its computational framework.

Option E: SCIMC– No such Python library exists; it appears to be a distractor.

PyMC’s primary strength is its ability to let data scientists define models in aprobabilistic programming style, making it easier to represent uncertainties and hidden variables in data. This aligns with DASCA’s emphasis on ensuring data scientists understand bothstatistical foundationsand thetools required to implement them programmatically.

In practice, PyMC is often used in applications such as:

Forecasting(e.g., time series with uncertainty bounds)

Causal inference(estimating hidden relationships in data)

Risk modeling(finance, healthcare, or supply chain domains)

Machine learning with uncertainty quantification

Thus,PyMCis the correct library for fitting Bayesian networks in Python.

Customer Lifetime Value (CLTV) is a predictive metric estimating the total revenue a business can reasonably expect from a customer during their entire relationship.

Statement i: Correct. Many organizations calculate CLTV using historic transactional data, often looking at sales records over the past 12–18 months to establish baselines.

Statement ii: Correct. The primary purpose of CLTV is to help marketing, sales, and retail teams understand customer value, enabling them to allocate budgets effectively for retention, promotions, and personalized marketing.

Thus, both statements are correct → Option C (Both i and ii).

The Hadoop ecosystem consists of multiple components, but the two core components that define Hadoop are:

HDFS (Hadoop Distributed File System): Provides fault-tolerant, scalable storage across distributed clusters. It is the backbone for storing massive datasets in a distributed fashion.

MapReduce Framework: Provides the parallel computing and data processing layer in Hadoop, enabling batch analysis over distributed datasets.

Option A: Correct, HDFS is essential.

Option B: Correct, MapReduce is essential.

Option C: Incorrect, Spark is a newer processing framework, but it is not originally part of Hadoop core.

Option D: Correct answer since both HDFS and MapReduce are considered the fundamental parts of Hadoop.

Option E: Incorrect, because Spark is not a core Hadoop component (though it integrates with Hadoop).