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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 zero values? a)0.018 b)0.982 c)0.989 d)0.976 Answer is b). Can you explain?
Most Upvoted Answer
If X~P(m) and its coefficient of variation is 50,what is the probabili...
So, the formula for coefficient of variation is given by -
COV = (SD/Mean) X 100
Now, we know that COV is 50% (it is always assumed that the COV is a percentage unless otherwise mentioned)
so by the above formula -
50 = (√m / m) X 100 (This is because mean =variance = m, in a Poisson distribution)
now when you simplify this further ,
you will get √m= 2 , therefore m=4
Now with m=4… we can solve the probability function in a Poisson distribution given by (e^-m . m^x)/X!
Now with this info,we need to find P(X>0).
however, P(x>o) = 1- P(X=0)
= 1- (e^-4 . 4^0)/ 0!
=1 - (1/e^4)
= 1- 0.01832
= 0.982
COV = (SD/Mean) X 100
Now, we know that COV is 50% (it is always assumed that the COV is a percentage unless otherwise mentioned)
so by the above formula -
50 = (√m / m) X 100 (This is because mean =variance = m, in a Poisson distribution)
now when you simplify this further ,
you will get √m= 2 , therefore m=4
Now with m=4… we can solve the probability function in a Poisson distribution given by (e^-m . m^x)/X!
Now with this info,we need to find P(X>0).
however, P(x>o) = 1- P(X=0)
= 1- (e^-4 . 4^0)/ 0!
=1 - (1/e^4)
= 1- 0.01832
= 0.982
Community Answer
If X~P(m) and its coefficient of variation is 50,what is the probabili...
Solution:
Given, X ~ P(m) and coefficient of variation = 50
The coefficient of variation of a Poisson distribution is given by the formula:
CV = sqrt(m)
where m is the mean of the Poisson distribution.
Therefore, sqrt(m)/m = 50/100
Solving for m, we get:
m = 4
Now, we need to find the probability that X assumes only non-zero values.
P(X > 0) = 1 - P(X = 0)
The probability mass function of a Poisson distribution is given by:
P(X = k) = (e^-m * m^k) / k!
Therefore, P(X = 0) = e^-4 = 0.0183 (approx.)
Hence, the probability that X assumes only non-zero values is:
P(X > 0) = 1 - P(X = 0) = 1 - 0.0183 = 0.9817 (approx.)
Therefore, the answer is b) 0.982.
Summary:
- Given X~P(m) and coefficient of variation = 50.
- Using formula, sqrt(m)/m = 50/100, we get m = 4.
- P(X > 0) = 1 - P(X = 0).
- Using probability mass function, we get P(X = 0) = e^-4 = 0.0183 (approx.).
- Therefore, the probability that X assumes only non-zero values is P(X > 0) = 1 - P(X = 0) = 1 - 0.0183 = 0.9817 (approx.).
- Hence, the answer is b) 0.982.
Given, X ~ P(m) and coefficient of variation = 50
The coefficient of variation of a Poisson distribution is given by the formula:
CV = sqrt(m)
where m is the mean of the Poisson distribution.
Therefore, sqrt(m)/m = 50/100
Solving for m, we get:
m = 4
Now, we need to find the probability that X assumes only non-zero values.
P(X > 0) = 1 - P(X = 0)
The probability mass function of a Poisson distribution is given by:
P(X = k) = (e^-m * m^k) / k!
Therefore, P(X = 0) = e^-4 = 0.0183 (approx.)
Hence, the probability that X assumes only non-zero values is:
P(X > 0) = 1 - P(X = 0) = 1 - 0.0183 = 0.9817 (approx.)
Therefore, the answer is b) 0.982.
Summary:
- Given X~P(m) and coefficient of variation = 50.
- Using formula, sqrt(m)/m = 50/100, we get m = 4.
- P(X > 0) = 1 - P(X = 0).
- Using probability mass function, we get P(X = 0) = e^-4 = 0.0183 (approx.).
- Therefore, the probability that X assumes only non-zero values is P(X > 0) = 1 - P(X = 0) = 1 - 0.0183 = 0.9817 (approx.).
- Hence, the answer is b) 0.982.
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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 zero values? a)0.018 b)0.982 c)0.989 d)0.976 Answer is b). Can you explain?
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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 zero values? a)0.018 b)0.982 c)0.989 d)0.976 Answer is b). Can you explain? 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 zero values? a)0.018 b)0.982 c)0.989 d)0.976 Answer is b). Can you explain? 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 zero values? a)0.018 b)0.982 c)0.989 d)0.976 Answer is b). Can you explain?.
If X~P(m) and its coefficient of variation is 50,what is the probability that X would assume only non zero values? a)0.018 b)0.982 c)0.989 d)0.976 Answer is b). Can you explain? 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 zero values? a)0.018 b)0.982 c)0.989 d)0.976 Answer is b). Can you explain? 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 zero values? a)0.018 b)0.982 c)0.989 d)0.976 Answer is b). Can you explain?.
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