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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?
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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.
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If X~ P(m) and its coefficient of variation is 50,what is the probabil...
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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?
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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?.
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