Chapter 6
Distribution Theory
6.1 INTRODUCTION
In this chapter we will mainly focus on the derivation of the distribution of a function of
random variables. The primary attention will be given to three methods among others.
They are: (i) The distribution

Chapter 3
RANDOM VARIABLES AND THEIR DISTRIBUTIONS
3.1 INTRODUCTION
In many occasions, when we perform experiments we are no more interested in the
outcomes of the experiments rather we want to assign numerical values to the outcomes
of the experiments. F

Chapter 8
Convergence of Random Variables
8.1 INTRODUCTION
In probability and statistics, it is often necessary to consider the distribution of a random
variable that is itself a function of several random variables. For example a sample mean
\
"
8
8
\3 i

Chapter 9
Laws of Large Numbers and Central Limit Theorem
9.1 INTRODUCTION
Let \8 be a sequence of random variables. Suppose that W8 \" \# \8
8 " # In this chapter we will study the following questions: Do there exists two
sequences of constants -8 and .

INTRODUCTION TO PROBABILITY AND STATISTICS
CHAPTER 2
Notations:
n
Summation: xi = x1 + x2 +
i =1
+ xn .
i =1
n
n
Product:
n
c = nc
x = ( x )( x ) ( x ) . c = c
i
i =1
1
2
n
n
i =1
n
Union:
A = AA A A
i
1
2
3
n
.
i =1
n
Intersection:
A = AA A A
i
1
2
3
n

Chapter 4
SOME SPECIAL
DISCRETE AND CONTINUOUS DISTRIBUTIONS
4.1 INTRODUCTION
There are some univariate distributions which play a central role in statistical theory and
practice. In this chapter we study some widely used univariate discrete and continuou

Chapter 7
Probability Inequalities
7.1 INTRODUCTION
We noted earlier that, to calculate probabilities, one needs either probability distribution
function or probability functions or probability density functions. For some random it
may not be possible to

Chapter 5
JOINTLY DISTRIBUTED RANDOM VARIABLES
5.1 INTRODUCTION
So far, we have studied distribution of only single random variables. In many situations it
is necessary to consider two or more random variables simultaneously. The joint
probability distrib