Properties of Probability
Probability of the Empty Set
Theorem (Probability of the empty set)
. In may cases, is not the only event with probability 0.
Compliment Rule
Theorem (Complement Rule)
For any
, .
Monotonicity Property
Theorem (Monotonicity)
Suppose
and are 2 events such that . Then .
The Numeric Bound
Theorem (Numeric bound)
It immediately follows from the monotonicity property that for any event
, .
Inclusion - Exclusion
Theorem (Inclusion-Exclusion)
If
and are two events, then
Sources
- Wasserman, L. (2010). All of Statistics: A concise Course in Statistical Inference. Chapter 1.