If X and Y are two random variables then V(x+y) is

Option c: V(x) + V(y) + 2Cov(x,y). Solution: For any two random variables X and Y , the variance of their sum is given by the formula: Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y) . In the given notation: V(x+y) = V(x) + V(y) + 2Cov(x,y) . Hence, Option C is the correct answer.

If $X$ and $Y$ are two random variables then $V(x+y)$ is

The correct answer is Option c: $V(x) + V(y) + 2Cov(x,y)$. For any two random variables $X$ and $Y$, the variance of their sum is given by the formula: $\text{Var}(X+Y) = \text{Var}(X) + \text{Var}(Y) + 2\text{Cov}(X,Y)$. In the given notation: $V(x+y) = V(x) + V(y) + 2\text{Cov}(x,y)$. Hence, **Option C** is the correct answer.

ProbabilityMCQMTP June 24 Series IIQuestion 2850 of 295

All Questions

If $\displaystyle X$ and $\displaystyle Y$ are two random variables then $\displaystyle V(x+y)$ is

Options

\displaystyle V(x) + V(y)

\displaystyle V(x) + V(y) - 2Cov(x,y)

\displaystyle V(x) + V(y) + 2Cov(x,y)

\displaystyle V(x) - V(y)

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Correct Answer

✅ Option c — $\displaystyle V(x) + V(y) + 2Cov(x,y)$

All Options:

A $\displaystyle V(x) + V(y)$
B $\displaystyle V(x) + V(y) - 2Cov(x,y)$
C $\displaystyle V(x) + V(y) + 2Cov(x,y)$
D $\displaystyle V(x) - V(y)$

Detailed Solution & Explanation

For any two random variables

\displaystyle X

and

\displaystyle Y

, the variance of their sum is given by the formula:

\displaystyle \text{Var}(X+Y) = \text{Var}(X) + \text{Var}(Y) + 2\text{Cov}(X,Y)

. In the given notation:

\displaystyle V(x+y) = V(x) + V(y) + 2\text{Cov}(x,y)

. Hence, **Option C** 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.

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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.

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If X\displaystyle XX and Y\displaystyle YY are two random variables then V(x+y)\displaystyle V(x+y)V(x+y) is