A random variable X follows Binomial Distribution With E(x)=2 and V(x)=1.2 , then the value of n is

Option c: 5. Solution: For a Binomial Distribution: E(X) = np = 2 and V(X) = npq = 1.2 . Step 1: Find q : q = V(X)/E(X) = 1.2/2 = 0.6 Step 2: Find p : p = 1 - q = 1 - 0.6 = 0.4 Step 3: Find n : n = E(X)/p = 2/0.4 = 5 Hence, Option C is the correct answer.

A random variable $X$ follows Binomial Distribution With $E(x)=2$ and $V(x)=1.2$, then the value of $n$ is

The correct answer is Option c: $5$. For a Binomial Distribution: $E(X) = np = 2$ and $V(X) = npq = 1.2$. **Step 1:** Find $q$: $$q = \frac{V(X)}{E(X)} = \frac{1.2}{2} = 0.6$$ **Step 2:** Find $p$: $$p = 1 - q = 1 - 0.6 = 0.4$$ **Step 3:** Find $n$: $$n = \frac{E(X)}{p} = \frac{2}{0.4} = 5$$ Hence, **Option C** is the correct answer.

Theoretical DistributionsMCQMTP Sep 24 Series IQuestion 3477 of 230

All Questions

A random variable $\displaystyle X$ follows Binomial Distribution With $\displaystyle E(x)=2$ and $\displaystyle V(x)=1.2$ , then the value of $\displaystyle n$ is

Options

\displaystyle 8

\displaystyle 2

\displaystyle 5

DNone of these

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Correct Answer

✅ Option c — $\displaystyle 5$

All Options:

A $\displaystyle 8$
B $\displaystyle 2$
C $\displaystyle 5$
DNone of these

Detailed Solution & Explanation

For a Binomial Distribution:

\displaystyle E(X) = np = 2

and

\displaystyle V(X) = npq = 1.2

. **Step 1:** Find

\displaystyle q

q = \frac{V(X)}{E(X)} = \frac{1.2}{2} = 0.6

**Step 2:** Find

\displaystyle p

p = 1 - q = 1 - 0.6 = 0.4

**Step 3:** Find

\displaystyle n

n = \frac{E(X)}{p} = \frac{2}{0.4} = 5

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

About This Chapter: Theoretical Distributions

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Binomial, Poisson, Normal Distribution

This chapter covers Binomial, Poisson, Normal Distribution and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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A random variable X\displaystyle XX follows Binomial Distribution With E(x)=2\displaystyle E(x)=2E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2V(x)=1.2, then the value of n\displaystyle nn is