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Since we can compute the mean and the standard deviation of a set of random variables, why do we use Maximum Likelihood Estimation to estimate these parameters?

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  • $\begingroup$ The MLE of a normal RV consists, indeed, in the empirical mean and variance. Where did you encounter the use of MLE to estimate a normal distribution parameters? $\endgroup$ – Romain Reboulleau Nov 12 '19 at 19:55
  • $\begingroup$ @RomainReboulleau In all materials I checked. See Theodoridis, S., & Koutroumbas, K. “Pattern recognition. ” Fourth Edition, 9781597492720, 2008 $\endgroup$ – Younes Nov 12 '19 at 20:00

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