Working Notes: a commonplace notebook for recording & exploring ideas.
Home. Site Map. Subscribe. More at expLog.

Stats

• 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 n_1, n_2, ..., n_r outcomes Overall, there are n_1 * n_2 * ... * 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

— Kunal