# 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

- 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

- Handout