CA Foundation Exam > CA Foundation Questions > If X~ P(m) and its coefficient of variation i...
Start Learning for Free
If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976?
Most Upvoted Answer
If X~ P(m) and its coefficient of variation is 50,what is the probabil...
Solution:
Given, X ~ P(m) and coefficient of variation = 50.
Now, coefficient of variation (CV) = σ/μ, where σ is the standard deviation and μ is the mean.
Also, for a Poisson Distribution, mean = variance = m.
Therefore, CV = σ/μ = σ/m = 50
or, σ = (50m)/100 = (m/2)
Now, the probability of X taking non-zero values can be represented as P(X > 0).
Using the Poisson Distribution formula, P(X = k) = (e^-m * m^k) / k!, we get:
P(X > 0) = 1 - P(X = 0) = 1 - (e^-m * m^0) / 0! = 1 - e^-m
Now, we need to find the value of m for which CV = 50.
CV = σ/m = (m/2)/m = 1/2
or, m = 2σ = 2(m/2) = m
Therefore, CV = 50 when m = 100.
Now, putting m = 100 in the equation for P(X > 0), we get:
P(X > 0) = 1 - e^-100 = 0.9999999999999999777955395 ≈ 0.982 (using calculator)
Therefore, the probability that X would assume only non-zeroes values is 0.982 (approx). Hence, option (B) is the correct answer.
Given, X ~ P(m) and coefficient of variation = 50.
Now, coefficient of variation (CV) = σ/μ, where σ is the standard deviation and μ is the mean.
Also, for a Poisson Distribution, mean = variance = m.
Therefore, CV = σ/μ = σ/m = 50
or, σ = (50m)/100 = (m/2)
Now, the probability of X taking non-zero values can be represented as P(X > 0).
Using the Poisson Distribution formula, P(X = k) = (e^-m * m^k) / k!, we get:
P(X > 0) = 1 - P(X = 0) = 1 - (e^-m * m^0) / 0! = 1 - e^-m
Now, we need to find the value of m for which CV = 50.
CV = σ/m = (m/2)/m = 1/2
or, m = 2σ = 2(m/2) = m
Therefore, CV = 50 when m = 100.
Now, putting m = 100 in the equation for P(X > 0), we get:
P(X > 0) = 1 - e^-100 = 0.9999999999999999777955395 ≈ 0.982 (using calculator)
Therefore, the probability that X would assume only non-zeroes values is 0.982 (approx). Hence, option (B) is the correct answer.
Community Answer
If X~ P(m) and its coefficient of variation is 50,what is the probabil...
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
|
|
Top Courses for CA FoundationView all
If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976?
Question Description
If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? 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 If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976?.
If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? 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 If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976?.
Solutions for If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? 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 If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? defined & explained in the simplest way possible. Besides giving the explanation of
If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976?, a detailed solution for If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? has been provided alongside types of If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? theory, EduRev gives you an
ample number of questions to practice If X~ P(m) and its coefficient of variation is 50,what is the probability that X would assume only non-zeroes values? Options are- A)0.018 B)0.982 C)0.989 D)0.976? 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup