Theoretical DistributionsMCQMTP May 18Question 3514 of 230
All Questions

Which one is not a condition of Poisson model

Options

Athe probability of having failures in a small time interval is constant
Bthe probability of having success more than one in a small time interval is very small
Cthe probability of having success in this time interval is independent of time 't' as well as earlier success
Dthe probability of having success in a small time interval (t,t+td)\displaystyle (t, t+td) is Kt\displaystyle Kt for a positive constant K\displaystyle K.
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Correct Answer

✅ Option a — the probability of having failures in a small time interval is constant

All Options:

  • Athe probability of having failures in a small time interval is constant
  • Bthe probability of having success more than one in a small time interval is very small
  • Cthe probability of having success in this time interval is independent of time 't' as well as earlier success
  • Dthe probability of having success in a small time interval (t,t+td)\displaystyle (t, t+td) is Kt\displaystyle Kt for a positive constant K\displaystyle K.

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Detailed Solution & Explanation

Let us analyze the conditions of the Poisson model: - In a Poisson process, the probability of having a success in a small time interval dt\displaystyle dt is proportional to the length of the time interval, i.e., w⋅dt\displaystyle w \cdot dt, where w\displaystyle w is a constant. Thus, the probability itself is not constant; it depends on the length of the interval. Also, the model specifies success, not failure, in this context. Therefore, Option A is not a condition of the Poisson model. - The probability of having more than one success in a small time interval is very small (negligible), which is a valid condition (Option B). - The probability of a success in a time interval is independent of the time t\displaystyle t and of earlier successes, which is the independence condition (Option C). - The probability of having success in a small time interval is proportional to the interval length, i.e., K⋅dt\displaystyle K \cdot dt (Option D, though with a minor typo in the textbook notation writing Kt\displaystyle Kt instead of K⋅dt\displaystyle K \cdot dt). Thus, Option A is not a condition of the Poisson model. 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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