I was thinking about MLE estimates and I stumbled on to something interesting Smile

Lets say I give you 100 normal random variables from a unknown mean distribution and known variance. Call them y1,y2,y3,…. How do you calculate MLE ?

One boring way is to compute the joint likelihood, differentiate with respect to mu, equate to  0 and find that MLE is mean of observations.

Second cool way is just do this