Probability and Statistics with
Reliability, Queuing and Computer
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 3 part a: Continuous Random Variables
Dept. of Electrical & Computer Engineering
2.4 Cumulative Distribution Function (CDF)
The cumulative distribution function of random variable X is
F X ( x) P[ X x]
For any real number x, the CDF is the probability that the random variable
X is no larger than x.
For all b a
F X (b) F X (a) P
Probability of Axioms
P[ ] Indicates the probability of an event.
For any events A , P A 0
P[ S ] 1
For any countable collection A1 , A2 ,. of mutually exclusive event
o Definitions establish the logic of probability theory.
o Axioms are facts that we accepts without proof.
o Theorems are consequences of definitions and axioms.
Set: Collection of things
Ex) How to define a set with
P A B :
Probability of A given B
Probability of A conditioned on B
P A B
P A B
P AB P B P A B
P B | A
P A | B P B