I was going through the definition of Kurtosis and there I found that it is possible that given two 1D normal distributions with the same mean and variance, they can have a different shapes. I found this concept counter-intuitive, as the normal distribution is governed by mean & standard deviation?
2026-04-08 14:33:47.1775658827
Is it possible that two 1-D Normal distributions, with equal mean and variance, can have different shapes?
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I believe your intuition is correct. A 1D normal distribution always has a kurtosis=3. Other 1D distributions will have different values of kurtosis depending on the specific shape of that distribution, but they won't be normal. More details here: https://en.wikipedia.org/wiki/Kurtosis
I hope this helps.