Random Variables MCQs

Prepare for Random Variables MCQs with verified questions, past-paper solutions, and conceptual explanations for CSS, PMS, FPSC, PPSC, and NTS examinations.

11 Solved Questions • 9 Mins Practice • Updated for 2026 Competitive Exams
MCQS
2026 Solved Edition · Updated October 2026 · Verified Editorial Standards

Welcome to the verified preparation module for Random Variables MCQs on McqsMind. This comprehensive set offers solved multiple-choice questions with answers, detailed explanations, and authentic past-paper style questions aligned with the latest syllabus of Probability Theory (Mathematics).

100% Verified Answer Keys CSS, PMS, FPSC, PPSC, NTS Ready 2026/2027 Syllabus Guidelines

Direct Definition & Conceptual Scope

AEO Verified

Random Variables constitutes an essential examination topic within Mathematics, evaluating theoretical principles, historical context, and practical problem-solving applications. On MCQsMind, candidates practice verified past-paper solutions, conceptual breakdowns, and syllabus-aligned questions tailored for CSS, PMS, and competitive screening examinations.

Solved Questions

Practice with answers, explanations, and exam-focused revision notes.

11 MCQs Page 1

High-Yield Exam Revision Cheat Sheet & Mnemonics

Essential exam standard definitions and formulas for rapid 2-minute revision

High-Frequency Articles
  • Art. 6: High Treason
  • Art. 9: Security of Person
  • Art. 19-A: Right to Information
  • Art. 25-A: Free Education (5–16 yrs)
Federalism & Provinces
  • Art. 140-A: Local Government
  • Art. 153: Council of Common Interests
  • Art. 160: National Finance Commission
  • Art. 175-A: Judicial Commission (JCP)
Islamic Provisions
  • Art. 2: Islam as State Religion
  • Art. 2A: Objectives Resolution Substantive
  • Art. 203: Federal Shariat Court (FSC)
  • Art. 228: Council of Islamic Ideology

Topic Notes: Random Variables

Quick Revision 3 min read 15 key points
Section 1 of 5

1 1. Fundamentals of Random Variables

4 points
  • Definition
    Random Variable: A function that maps outcomes of a sample space to real numbers, allowing for the mathematical analysis of probabilistic events.
  • Definition
    Discrete Random Variable: A variable that takes on a countable number of distinct values, such as the result of a coin flip or the number of students in a class.
  • Definition
    Continuous Random Variable: A variable that can take any value within a specific interval or range, such as height, weight, or time, represented by an uncountable set of values.
  • Theory
    Cumulative Distribution Function (CDF): Defined as F(x) = P(X ≤ x), it represents the probability that a random variable X takes a value less than or equal to x for all real numbers.
Section 1 / 5
Swipe or tap Prev / Next to revise all sections.

Want adaptive tracking for this topic?

Login to save wrong answers to your Mistake Bank and build your weakness heatmap automatically.

Session Progress 0 / 0 Solved
Reveal answers to start tracking your session progress!
1
What is the expected value of the sum of two random variables E[X + Y]?
Moderate · 64% Accuracy
Share
2
Which inequality provides an upper bound on the probability that a random variable deviates from its mean by more than a specified amount?
Moderate · 64% Accuracy
Share
3
What is the range of the correlation coefficient between two random variables X and Y?
Moderate · 64% Accuracy
Share
4
For a standard normal distribution, what is the mean and variance?
Moderate · 64% Accuracy
Share
5
What is the characteristic property of a Poisson random variable?
Moderate · 64% Accuracy
Share
6
Which distribution describes the number of successes in a fixed number of independent Bernoulli trials?
Moderate · 64% Accuracy
Share
7
What is the relationship between the variance of a random variable X and the variance of a constant cX?
Moderate · 64% Accuracy
Share
8
What does the variance of a random variable measure?
Moderate · 64% Accuracy
Share
9
Which property must a function f(x) satisfy to be a valid probability density function for a continuous random variable?
Moderate · 64% Accuracy
Share
10
What is the expected value E[X] of a discrete random variable X with probability mass function p(x)?
Moderate · 64% Accuracy
Share
Pedagogical Syllabus Blueprint

Random Variables MCQs: Preparation Strategy & Exam Blueprint

Examination Weightage & Commission Distribution

In Pakistan's premier competitive examinations—including the Federal Public Service Commission (FPSC General Recruitment & CSS MPT), Punjab Public Service Commission (PPSC Lecturer, Tehsildar & PMS Screening), KPPSC, SPSC, and BPSC—questions derived from Random Variables MCQs consistently constitute a decisive 10% to 25% weightage of the Probability Theory paper. Testing agencies frequently evaluate both foundational factual recall and deeper analytical comprehension, requiring aspirants to master key dates, statutory articles, constitutional clauses, and thematic definitions.

High-Yield Conceptual Pillars & Distractor Analysis

Historical trend analysis across past five-year examination cycles demonstrates that examiner traps frequently involve closely matched numerical alternatives, chronologically contiguous treaties, and semantic subtleties in statutory phraseology. When preparing Random Variables MCQs, candidates must deliberately review the underlying rationale provided for every question rather than merely memorizing raw answer options. Understanding why incorrect distractors fail is the most reliable predictor of achieving top percentiles in computerized and optical mark recognition (OMR) screening tests.

Negative Marking Mitigation & Time Management Protocol

For examinations enforcing negative marking penalties (such as PPSC's 0.25-mark deduction per erroneous response or NTS gatekeeper quotas), an aggressive elimination technique must be deployed. Candidates should systematically rule out improbable options first to elevate probability thresholds from 25% to 50% or 100%. Allocating an average of 45 to 60 seconds per item during mock trials builds the psychological stamina and cognitive precision required to complete 100-question papers within official 90-minute time limits.

Recommended Reference Sources & Statutory Reading

To achieve definitive conceptual mastery in Mathematics, candidates are advised to cross-reference our solved explanations with primary gazettes, statutory texts, and canonical academic textbooks. Verifying controversial questions against authentic official repositories guarantees that prospective civil servants and professional candidates present incontestable answers during both optical paper evaluations and viva voce departmental interviews.