Expectation, Variance, Covariance and Correlation Practice Questions for GATE DA: 0+ Solved Questions with Step-by-Step Solutions

Solve 0+ Expectation, Variance, Covariance and Correlation practice questions for GATE DA with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Expectation, Variance, and Covariance

Your Journey Through This Chapter

Expectation and Linearity
The center of mass. LOTUS and the powerful linearity property.

Variance and Standard Deviation
Measuring the spread. The computational formula and transformation rules.

Covariance and Correlation
Joint variability. Distinguishing between independence and being uncorrelated.

Transformations and Sums
Variance of sums, products of independent variables, and linear transformations.

The Heart of Random Variables: Expectation

The Expectation (or expected value, or mean) of a random variable $X$ , denoted as $E [X]$ or $μ_{X}$ , represents the long-run average value or the "center of mass" of its distribution.

For Discrete Random Variables:

E [X] = x \sum x \cdot P (X = x)

For Continuous Random Variables:

E [X] = \int_{- \infty}^{\infty} x \cdot f_{X} (x) d x

Key Intuition: Expectation is a weighted average. Values with higher probability pull the expectation closer to themselves. It does not necessarily have to be a value that $X$ can actually take (for example, the expected value of a fair die roll is $3.5$ ).

Login to view the complete practice questions and solutions

Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

Why MastersUp

Personalised first. High quality throughout.

Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

Built around you, not around a syllabus PDF

Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

Revision that hits your weak spots

We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

Questions calibrated to the real exam

Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

Notes written for recall, not for volume

Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

One place for everything

Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

Honest progress

No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

Unlock the whole course

Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

View all plans Start free