University:
Massachusetts Institute of Technology
Course:
18.05 | Introduction to Probability and Statistics
Academic year:

2024
Views:

386

Pages:

5
Author:

do3ran7ut

Midterm Review Topic 1. Basics sample points = individual outcomes of an exp. sample Space = set of all sample pts. Omega random / probabilistic event = anything that can be repeated Omega = {HH, HT, TH, TT} -> sample points Omega -> sample space rep. (coin tosses?) event = subset of Omega For any event A, P(A) = Sum P(omega) for all omega in A In equally likely: P(X) = (# sample points in X) / (# sample points in Omega) -> 1/N for all omega Topic 2: Unions, Intersections, Counting Committee Problem: (n choose r) (committees of size r from n) = n! / (r! (n-r)!) -> due to Pascal's triangle U = union, intersection = intersection Addition Formula P(A U B) = P(A) + P(B) - P(A intersection B) P(A U B) = P(A) + P(B) for disjoint (n choose r) = n! / (r! (n-r)!) n! -> arrange n objs with order n(n-1)...(n-r+1) -> choose r from n, order imp. (n choose r) -> choose r order not imp n^k -> choose r from n if can choose w/ replacement (n+k-1 choose k-1) -> n objects to k cells/bins