Theoretical DistributionsMCQMTP Sep 24 Series IIQuestion 3479 of 230
All Questions

If X\displaystyle X is a binomial variable with parameters n\displaystyle n and p\displaystyle p, then X\displaystyle X can assume

Options

Aany value between 0\displaystyle 0 and n\displaystyle n.
Bany value between 0\displaystyle 0 and n\displaystyle n, both inclusive.
Cany whole number between 0\displaystyle 0 and n\displaystyle n, both inclusive.
Dany number between 0\displaystyle 0 and infinity.
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Correct Answer

✅ Option c — any whole number between 0\displaystyle 0 and n\displaystyle n, both inclusive.

All Options:

  • Aany value between 0\displaystyle 0 and n\displaystyle n.
  • Bany value between 0\displaystyle 0 and n\displaystyle n, both inclusive.
  • Cany whole number between 0\displaystyle 0 and n\displaystyle n, both inclusive.
  • Dany number between 0\displaystyle 0 and infinity.

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Detailed Solution & Explanation

A Binomial random variable X\displaystyle X represents the number of successes in n\displaystyle n independent Bernoulli trials. The number of successes must be a **whole number** (non-negative integer): 0,1,2,3,…,n\displaystyle 0, 1, 2, 3, \ldots, n. - It cannot be a fraction or decimal. - The minimum value is 0\displaystyle 0 (no successes) and the maximum value is n\displaystyle n (all successes), both inclusive. - It cannot go to infinity since there are only n\displaystyle n trials. Therefore, X\displaystyle X can assume any **whole number** between 0\displaystyle 0 and n\displaystyle n, both inclusive. 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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