Theoretical DistributionsMCQMTP Nov 18Question 3435 of 230
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The mean of binomial distribution is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — Always more than its variance

All Options:

  • AAlways more than its variance
  • Balways equal to variance
  • Cless than its variance
  • Dalways equal to Standard deviation

Detailed Solution & Explanation

**Comparing Mean and Variance in Binomial Distribution**\n\nFor a Binomial Distribution B(n,p)\displaystyle B(n, p):\ntextMean=np\Mean=np\displaystyle \text{Mean} = np\ntextVariance=npq\Variance=npq\displaystyle \text{Variance} = npq\n\n**Ratio of Mean to Variance:**\nfractextMeantextVariance=fracnpnpq=frac1q\textMeantextVariance\displaystyle \frac{\\text{Mean}}{\\text{Variance}} = \npnpq\displaystyle \frac{np}{npq} = \1q\displaystyle \frac{1}{q}\n\nSince $0 < q < 1(as\displaystyle (asq = 1 - p\displaystyle and &#36;0 < p < 1):\nfrac1q>1\1q\displaystyle \frac{1}{q} > 1\nRightarrowtextMean>textVariance\\Rightarrow \Mean\displaystyle \text{Mean} > \Variance\displaystyle \text{Variance}\n\n**Example:** B(10,0.6)\displaystyle B(10, 0.6): Mean =6\displaystyle = 6, Variance =2.4\displaystyle = 2.4. Clearly $6 > 2.4$.\n\nThis is always true — the mean of a binomial distribution is **always greater** than its variance.\n\nHence, **Option A** 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

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

When p=0.5\displaystyle p=0.5, the binomial distribution is

If mean and standard deviation of a binomial distribution is $10and\displaystyle and2respectively,\displaystyle respectively,q$ will be

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 $0.5$, the Binomial Distribution is:

For a Poisson distribution,

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