CA Foundation Exam > CA Foundation Questions > For a Poisson distribution,a)mean and standar...
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For a Poisson distribution,
- a)mean and standard deviation are equal.
- b)mean and variance are equal.
- c)standard deviation and variance are equal.
- d)both (a) and (b).
Correct answer is option 'B'. Can you explain this answer?
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For a Poisson distribution,a)mean and standard deviation are equal.b)m...
Mean and Variance of Poisson Distribution:
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.
The mean and variance of a Poisson distribution are given by the parameter λ, which represents the average number of events that occur in the given interval.
- Mean: The mean of a Poisson distribution is equal to λ.
- Variance: The variance of a Poisson distribution is also equal to λ.
Explanation:
- Option (a): Mean and standard deviation are equal. This statement is not true for a Poisson distribution because the standard deviation of a Poisson distribution is equal to the square root of the variance, which is not equal to the mean.
- Option (b): Mean and variance are equal. This statement is true for a Poisson distribution because the mean and variance are both equal to the parameter λ.
- Option (c): Standard deviation and variance are equal. This statement is not true for a Poisson distribution because the standard deviation is the square root of the variance, and they are not equal to each other.
- Option (d): Both (a) and (b). This statement is not true because only option (b) is correct.
Conclusion:
In summary, the mean and variance of a Poisson distribution are equal, which means option (b) is the correct answer.
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.
The mean and variance of a Poisson distribution are given by the parameter λ, which represents the average number of events that occur in the given interval.
- Mean: The mean of a Poisson distribution is equal to λ.
- Variance: The variance of a Poisson distribution is also equal to λ.
Explanation:
- Option (a): Mean and standard deviation are equal. This statement is not true for a Poisson distribution because the standard deviation of a Poisson distribution is equal to the square root of the variance, which is not equal to the mean.
- Option (b): Mean and variance are equal. This statement is true for a Poisson distribution because the mean and variance are both equal to the parameter λ.
- Option (c): Standard deviation and variance are equal. This statement is not true for a Poisson distribution because the standard deviation is the square root of the variance, and they are not equal to each other.
- Option (d): Both (a) and (b). This statement is not true because only option (b) is correct.
Conclusion:
In summary, the mean and variance of a Poisson distribution are equal, which means option (b) is the correct answer.
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For a Poisson distribution,a)mean and standard deviation are equal.b)mean and variance are equal.c)standard deviation and variance are equal.d)both (a) and (b).Correct answer is option 'B'. Can you explain this answer?
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