Calculating the maximum likelihood estimates for the normal distribution shows you why we use the mean and standard deviation define the shape of the curve.
NOTE: This is another follow up to the StatQuests on Probability vs Likelihood
   • Probability is not Likelihood. Find o...   and Maximum Likelihood:    • Maximum Likelihood, clearly explained!!!  
Viewers asked for worked out examples, and this one is super mathy, but I just couldn't say "no"!

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0:00 Awesome song and introduction
0:45 Overview of the normal distribution equation
1:41 Example with one data point
5:38 Example with two data points
7:35 Example in 'n' data points
8:08 Solving for the MLEs for mu and sigma
18:54 Review of concepts

Correction:
2:39 I said likelihood=0.03 for mu=30, but mu=28 is in the equation.

#statquest #MLE #statistics