Theoretical DistributionsMCQMTP Apr 21Question 3451 of 230
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The mean of a binomial distribution with parameter n\displaystyle n and p\displaystyle p is

Options

An(1−p)\displaystyle n(1-p)
Bnp(1−p)\displaystyle np(1-p)
Cnp\displaystyle np
Dsqrtnp(1−p)\displaystyle \\sqrt{np(1-p)}
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Correct Answer

✅ Option c — np\displaystyle np

All Options:

  • An(1−p)\displaystyle n(1-p)
  • Bnp(1−p)\displaystyle np(1-p)
  • Cnp\displaystyle np
  • Dsqrtnp(1−p)\displaystyle \\sqrt{np(1-p)}

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Detailed Solution & Explanation

**Mean of Binomial Distribution** For a Binomial distribution B(n,p)\displaystyle B(n, p) where n\displaystyle n = number of trials and p\displaystyle p = probability of success: E(X)=textMean=npE(X) = \\text{Mean} = np **Derivation (brief):** E(X)=sumx=0nxbinomnxpxqn−x=npsumx=1nbinomn−1x−1px−1qn−x=np(p+q)n−1=npE(X) = \\sum_{x=0}^{n} x \\binom{n}{x} p^x q^{n-x} = np \\sum_{x=1}^{n} \\binom{n-1}{x-1} p^{x-1} q^{n-x} = np(p+q)^{n-1} = np **Checking options:** - Option A: n(1−p)=nq\displaystyle n(1-p) = nq — this is neither mean nor variance - Option B: np(1−p)=npq\displaystyle np(1-p) = npq — this is the **Variance** - Option C: np\displaystyle np — this is the **Mean** ✓ - Option D: sqrtnp(1−p)\displaystyle \\sqrt{np(1-p)} — this is the **Standard Deviation** 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.

More Questions from Theoretical Distributions

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

When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:

For a Poisson distribution,

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