If mean of the Poisson distribution is m, then standard deviation is equal to :

Question

Accepted Answer

In a Poisson distribution, the mean and the variance are both equal to the parameter $ m $. This is a fundamental property of the Poisson distribution. The standard deviation is the square root of the variance. Therefore, if the variance is $ m $, the standard deviation is $ \sqrt{m} $. This directly supports Option 2 as the correct answer.

Let's examine why the other options are incorrect:

1. **Option 1: m** - This option suggests that the standard deviation is equal to the mean. While the mean and variance of a Poisson distribution are equal, the standard deviation is not equal to the mean; it is the square root of the mean. Therefore, Option 1 is incorrect.

2. **Option 3: $ m^2 $** - This option implies that the standard deviation is the square of the mean. However, the standard deviation is the square root of the variance, not the square of the mean. Since the variance is $ m $, the standard deviation is $ \sqrt{m} $, not $ m^2 $. Thus, Option 3 is incorrect.

3. **Option 4: $ m(m-1) $** - This option suggests a formula that does not relate to the standard deviation of a Poisson distribution. The expression $ m(m-1) $ does not represent the standard deviation or any other standard measure in a Poisson distribution. Therefore, Option 4 is incorrect.

In conclusion, the correct answer is Option 2: $ \sqrt{m} $, because the standard deviation of a Poisson distribution is the square root of its mean, which is $ m $.