If X and Y are random variables having expected values as 4.5 and 2.5 respectively, then the expected value of (x-y) is

Option a: 2. Solution: By the linearity of expectation, the expected value of the difference between two random variables X and Y is the difference of their expected values: E(X-Y) = E(X) - E(Y) . Given: - E(X) = 4.5 - E(Y) = 2.5 We calculate: E(X-Y) = 4.5 - 2.5 = 2 . Matching with the options: - Option A: 2 - Option B: 7 - Option C: 6 - Option D: 0 Hence, Option A is the correct answer.

If $X$ and $Y$ are random variables having expected values as $4.5$ and $2.5$ respectively, then the expected value of $(x-y)$ is

The correct answer is Option a: $2$. By the linearity of expectation, the expected value of the difference between two random variables $X$ and $Y$ is the difference of their expected values: $E(X-Y) = E(X) - E(Y)$. Given: - $E(X) = 4.5$ - $E(Y) = 2.5$ We calculate: $E(X-Y) = 4.5 - 2.5 = 2$. Matching with the options: - Option A: $2$ - Option B: $7$ - Option C: $6$ - Option D: $0$ Hence, **Option A** is the correct answer.

ProbabilityMCQMTP Sep 24 Series IIQuestion 2851 of 295

All Questions

If $\displaystyle X$ and $\displaystyle Y$ are random variables having expected values as $\displaystyle 4.5$ and $\displaystyle 2.5$ respectively, then the expected value of $\displaystyle (x-y)$ is

Options

\displaystyle 2

\displaystyle 7

\displaystyle 6

\displaystyle 0

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle 2$

All Options:

A $\displaystyle 2$
B $\displaystyle 7$
C $\displaystyle 6$
D $\displaystyle 0$

Detailed Solution & Explanation

By the linearity of expectation, the expected value of the difference between two random variables

\displaystyle X

and

\displaystyle Y

is the difference of their expected values:

\displaystyle E(X-Y) = E(X) - E(Y)

. Given: -

\displaystyle E(X) = 4.5

\displaystyle E(Y) = 2.5

We calculate:

\displaystyle E(X-Y) = 4.5 - 2.5 = 2

. Matching with the options: - Option A:

\displaystyle 2

- Option B:

\displaystyle 7

- Option C:

\displaystyle 6

- Option D:

\displaystyle 0

Hence, **Option A** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

View Official ICAI Syllabus

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

Ready to Master Probability?

Practice all 295 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

If X\displaystyle XX and Y\displaystyle YY are random variables having expected values as 4.5\displaystyle 4.54.5 and 2.5\displaystyle 2.52.5 respectively, then the expected value of (x−y)\displaystyle (x-y)(x−y) is