# 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, …, nr outcomes Overall, there are n1 * n2 * … * nr 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