Kurtosis of non standard normal distribution

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Say if I have a X~N($\mu,\sigma^2$) Have I can find the kurtosis from kurtosis of standard normal distribution = 3?

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1 Answer

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All normal distributions can be seen as location- and scale-adjusted forms of a standard normal.

Since kurtosis is unaffected by scale and location changes, the kurtosis will not change, so is $3$ for all normal distributions (and the excess kurtosis is $0$ for those who think that way)

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