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Stats Notes

Lecture 1
- Handout
- Sample space
  
  Set of all possible outcomes of an experiment.
- Event
  
  Subset of sample space.
- Naive Definition of Probability
  
  P(A) = # favourable to a outcomes / # possible outcomes P = probability A = of Event A
- Counting
  - Multiplication Rule
    
    If there are experiments with n₁, n₂, …, n_r outcomes Overall, there are n₁ * n₂ * … * n_r outcomes for the combined experiment.
- Binomial Coefficient
  
  (n C k) = n! / (n-k)! k! Subsets of size k of groups n people if k <= n Motivated by manually counting out how we can choose people Order doesn't matter
- Full house: 3 cards of one rank, 2 of another. Eg (7, 7, 7, 10, 10)
  - Assume shuffled deck of cards
  - Numerator:
    - 3 of (13 C 1) ranks, which means 3 of 4 options - (4 C 3)
    - 2 of (12 C 1) ranks, and 2 of those (4 C 2)
    - 13 . (4 C 3) . 12 . (4 C 2)
  - Denominator: (52 C 5)
- If order does matter
  
  Sampling table: choose k objects from n objects
  
  x Order Matters Order Doesn't Matter
  
  Replacement n ^ k (n + k - 1 C k )
  
  No Replacement n! / k! n C k
  
  Eg. if I have a set of 1, 2, 3 Replacement with order doesn't matter: choosing 2 elements: 11, 22, 33, 12, 13, 23