Probability and Statistics with
Reliability, Queuing and Computer
Science Applications:
Second edition
by K.S. Trivedi
Publisher-John Wiley & Sons
Chapter 3 part a: Continuous Random Variables
Dept. of Electrical & Computer Engineering
Duke University
Ema
Lec 05
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
Lec 02
Set Algebra
Universal set
Set
Element
Probability
Sample space
Event
Outcome
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
Lec 01
Definitions
Axioms
Theorems
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
Lec 03
Conditional probability
P A B :
Probability of A given B
Probability of A conditioned on B
P AB
P A B
P B
P B
P AB
P A B
P AB P B P A B
Bays Theorem
P B | A
=
P A | B P B
P A
P AB
P B
P B
P A
P AB
=
=
P B
P B
P A
P BA
P A
Sequential ex