Expectation and Variance MCQs

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

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

Welcome to the verified preparation module for Expectation and Variance 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

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Expectation and Variance 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.

14 MCQs Page 1

High-Yield Exam Revision Cheat Sheet & Mnemonics

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Topic Notes: Expectation and Variance

Quick Revision 3 min read 15 key points
Section 1 of 4

1 1. Definition of Expected Value

4 points
  • Definition
    Expected Value (E[X]): The long-run average value of a random variable over many trials, calculated as the weighted average of all possible outcomes, where weights are their respective probabilities.
  • Theory
    Discrete Expectation: For a discrete random variable X, E[X] = Σ x * P(X=x), where the sum is taken over all possible values x in the sample space.
  • Theory
    Linearity of Expectation: E[aX + b] = aE[X] + b, regardless of whether X and Y are independent. This is a fundamental property used to simplify complex expected value calculations.
  • Fact
    Fair Die Expectation: For a fair six-sided die, the expected value is (1+2+3+4+5+6)/6 = 3.5. This demonstrates that the expected value does not have to be an outcome present in the sample space.
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1
If X is a random variable, what is E[aX] equal to?
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2
What does the standard deviation represent in relation to variance?
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3
For a binomial distribution with parameters n and p, what is the variance?
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4
What is the expected value of the sum of two random variables E[X + Y]?
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5
If E[X] = 5 and E[X^2] = 29, what is the variance of X?
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6
What is the variance of a uniform distribution on the interval [a, b]?
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7
For a fair six-sided die, what is the expected value of the outcome?
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8
Which of the following describes the behavior of variance under linear transformation?
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9
What is the expected value of a Poisson random variable with parameter lambda?
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10
If X and Y are independent random variables, what is the variance of their sum, Var(X + Y)?
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Pedagogical Syllabus Blueprint

Expectation and Variance 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 Expectation and Variance 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 Expectation and Variance 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.