Theoretical DistributionsMCQMTP May 19Question 3568 of 230
All Questions

For Poisson fitting to an observed frequency distribution

Options

Awe equate the Poisson parameter to the mean of the frequency distribution.
Bwe equate the Poisson parameter to the median of the distribution.
Cwe equate the Poisson parameter to the mode of the distribution
Dnone of these
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Correct Answer

✅ Option a — we equate the Poisson parameter to the mean of the frequency distribution.

All Options:

  • Awe equate the Poisson parameter to the mean of the frequency distribution.
  • Bwe equate the Poisson parameter to the median of the distribution.
  • Cwe equate the Poisson parameter to the mode of the distribution
  • Dnone of these

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Detailed Solution & Explanation

**Fitting a Poisson Distribution** **First Principles:** 1. The Poisson distribution is defined by a single parameter, m\displaystyle m (the mean rate of success). 2. To fit a Poisson distribution to an observed frequency distribution, we estimate the theoretical parameter m\displaystyle m using the sample data. 3. According to the method of moments, we equate the theoretical population mean to the observed sample mean: Theoretical Mean (m)=Observed Mean (xˉ)\text{Theoretical Mean } (m) = \text{Observed Mean } (\bar{x}) where xˉ=∑fixi∑fi\displaystyle \bar{x} = \frac{\sum f_i x_i}{\sum f_i}. **Conclusion:** We equate the Poisson parameter m\displaystyle m to the arithmetic mean of the observed frequency distribution. This corresponds to Option A. *Note:* Although some textbook keys list Option D, Option A is the mathematically correct statement. Hence, **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.

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