CA Foundation Exam > CA Foundation Questions > A binomial distribution with parameters m and...
Start Learning for Free
A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np is
- a)m → ∝.
- b)p → 0.
- c)m → ∝ and p → 0.
- d)m → ∝ and p → 0 so that mp remainsfinite..
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A binomial distribution with parameters m and p can be approximated by...
Binomial Distribution and Poisson Distribution
Binomial Distribution:
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. Let X be the number of successes in n trials, then X has a binomial distribution with parameters n and p, denoted by X~B(n,p)
Poisson Distribution:
The Poisson distribution is a discrete probability distribution that describes the number of occurrences of a rare event within a fixed interval of time or space. Let X be the number of occurrences of the event in the interval, then X has a Poisson distribution with parameter λ, denoted by X~Pois(λ).
Approximation of Binomial Distribution by Poisson Distribution
When n is large and p is small, it is often difficult and time-consuming to compute binomial probabilities. In such cases, we can approximate the binomial distribution by a Poisson distribution with parameter λ = np.
The conditions under which the binomial distribution can be approximated by a Poisson distribution are:
1. n is large
2. p is small
3. np is finite
In such cases, the Poisson distribution provides a good approximation to the binomial distribution.
Applying these conditions to the given options:
a) Incorrect: Only m is given, we cannot conclude anything about p.
b) Incorrect: Only p is given, we cannot conclude anything about m.
c) Incorrect: Only m is given, we cannot conclude anything about p.
d) Correct: The condition np is finite is satisfied. Therefore, we can approximate the binomial distribution with parameters m and p by a Poisson distribution with parameter λ = np = mp.
Binomial Distribution:
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. Let X be the number of successes in n trials, then X has a binomial distribution with parameters n and p, denoted by X~B(n,p)
Poisson Distribution:
The Poisson distribution is a discrete probability distribution that describes the number of occurrences of a rare event within a fixed interval of time or space. Let X be the number of occurrences of the event in the interval, then X has a Poisson distribution with parameter λ, denoted by X~Pois(λ).
Approximation of Binomial Distribution by Poisson Distribution
When n is large and p is small, it is often difficult and time-consuming to compute binomial probabilities. In such cases, we can approximate the binomial distribution by a Poisson distribution with parameter λ = np.
The conditions under which the binomial distribution can be approximated by a Poisson distribution are:
1. n is large
2. p is small
3. np is finite
In such cases, the Poisson distribution provides a good approximation to the binomial distribution.
Applying these conditions to the given options:
a) Incorrect: Only m is given, we cannot conclude anything about p.
b) Incorrect: Only p is given, we cannot conclude anything about m.
c) Incorrect: Only m is given, we cannot conclude anything about p.
d) Correct: The condition np is finite is satisfied. Therefore, we can approximate the binomial distribution with parameters m and p by a Poisson distribution with parameter λ = np = mp.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer?
Question Description
A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer?.
A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer?.
Solutions for A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A binomial distribution with parameters m and p can be approximated by a Poisson distribution with parameter m = np isa)m .b)p 0.c)m and p 0.d)m and p 0 so that mp remainsfinite..Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup