Are the mean and standard deviation equal in a perfect bell curve distribution?

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PastorThaddeusWinthrop

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If I have a normal distribution with zero skewness and kurtosis, should the standard deviation be the same as the mean?...ie with a coefficient of variation = 1.

EDIT: I asked what the mean and variance were when the *KURTOSIS* IS ZERO!
 
No. The mean ? may take any value in the real domain and so, in principle, may the standard deviation ?. There is no requirement for them to be equal.

The distribution which, by definition, has mean equal to variance is the Poisson distribution. Stated formally, "The expected value of a Poisson-distributed random variable is equal to ? and so is its variance."

For certain values of ?, the Poisson distribution can be approximated by the Normal. In that case, the mean and variance could be approximately equal, but that is a special case and the limiting conditions will not be met typically in Gaussian processes.

OK?
 
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