L07.8 The Hat Problem

MIT RES.6-012 Introduction to Probability, Spring 2018
Instructor: John Tsitsiklis

License: Creative Commons BY-NC-SA

[biswajitdas]

The way you say "factorial" ❤️

[akshaytak]

this question is mind-blowing and explains a lot of concepts, and Explained effortlessly by professor John

[alroyg]

but when we say E[Xi] to be the same for each person we are assuming that each person is the first to pick a hat and therefore probability is 1/n for each, otherwise the probability (which is the same expected value for indicator r.v.) would be 1/n for 1st, 1/(n-1) for 2nd and so forth and we couldn't get the simplification of E[X], as the total sum would be different. Most likely I'm wrong but I don't follow...
(btw: thanks for this material)

[tarunpahuja]

The algorithm Book CLRS has that hat question.

[tarunpahuja]

Just like random variables are dependent. You should have explained in the beginning that P(Second person getting hat) is also dependent on P(first person getting hat)

[rumanasultana-vf]

does everyone has the same probability of picking for the very first time?

[rudraprasadtarai]

no of XiXj, should not it be nC2.... that is (n^2-n)/2

[vintagegamer]

Yeah but what if they know what their hats look like?

[mindloop]

I dont think its a correct way to derive model for this kind of problem as we have to consider the fact that next person who is choosing the hat his probability of choosing his own hat depends on the probability of chosing hat by person before him... it doesnt make sense though

[mindloop]

why to make it so complicated when you have a easy solution..random variable taking values 0, 1 and 3 with their individual probabilities being 2/6, 3/6 and 1/6 respectively...the answer u will get 1

[sandeepraj]

This was probably the worst explained lecture in this series.