 
Summary: Com S 633: Randomness in Computation
Lecture 1 Scribe: A. Pavan
1 Probability
Each possible outcome of an experiment is called a sample point. The set of all sample points is
called sample space, denoted by
For example, in the experiment of 100 coin tosses, the sample
space is f0; 1g 100 . An event E is a subset of
For example in the above experiment, the set of
coins tosses with even number of heads is an event. Probability function P is a function
from
to
[0; 1] such that
P
x2
P (x) = 1. Probability of an event E is
P
x2E P (x). Two events A and B are
independent P r(A \ B) = P r(A) P r(B).
A random variable X is a function from sample space to the real numbers, X
:
