[Stat-110 Harvard] (google.com)

[Lecture 1] (https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PLCzY7wK5FzzPANgnZq5pIT3FOomCT1s36&index=0)

Tables for k of N Picks order matters ordering doesn’t matter
replacement n\^k n+k-1 C k
no replacement n *(n-1)*…. (n-k+1) nCk

[Lecture 2] (https://www.youtube.com/watch?v=FJd_1H3rZGg&list=PLCzY7wK5FzzPANgnZq5pIT3FOomCT1s36&index=1)

Tables for k of N Picks order matters ordering doesn’t matter
replacement n\^k n+k-1 C k
no replacement n *(n-1)*…. (n-k+1) nCk

$ \sum_{\forall i}{x_i^{2}} $

$ \theta$

[Lecture 3] (https://www.youtube.com/watch?v=LZ5Wergp_PA&list=PLCzY7wK5FzzPANgnZq5pIT3FOomCT1s36&index=2)

Birthday Problem:

Properties of Probability:

Demontmort Problem:

n card labelled 1,2,3…n

We are interested in P(A1 U P2 …U An)

P(Aj) = /n Since all postions are equally likely for a card lebelled j. $ P(A_1 Intersect A_2) = (n-2)!/n! = 1/n(n-1)

$ 1 - \divide_{1}{e}