Algebra of Sets and Counting Methods
The algebra of sets and counting methods are useful in understanding the basic
concepts of probability. These concepts are briefly reviewed from the point of
view of probability.
Sets and Elements of sets: The fundamen

2.6
Functions of Random Variables
The previous modules discussed basic properties of events defined in a given
sample space and the random variables used to represent those events. The
fundamental assumption that was made in those modules is that events c

2.5
Continuous Probability Distributions
The continuous probability distributions are used in a number of applications in
engineering. For example in error analysis, given a set of data or probability distribution,
it is possible to estimate the probabili

2.4
Discrete Probability Distributions
Modules
and
deal with general properties of random variables. Random
variables with special probability distributions are encountered in different fields
of science and engineering. Some specific discrete probability

2.3
Mathematical Expectation
The term expectation is used for the process of averaging when a random variable
is involved. It is the number used to locate the centre of the probability
distribution (p.m.f or p.d.f) of a random variable. A probability dist

2.2
Bivariate random variable
In the real life situations more than one variable effects the outcome of a random
experiment. For example, consider an electronic system consisting of two
components. Suppose the system will fail if both the components fail.

Unit 2
Probability distributions
2.1
Random Variable
While performing a random experiment we are mainly concerned with the
assignment and computation of probabilities of events. In many experiments we
are interested in some function of the outcomes of the

1.5
BayesTheorem and Its Applications
One of the important applications of the conditional probability is in the
computation of unknown probabilities on the basis of the information supplied by
the experiment or past records. For example, suppose an event

1.3.
Definitions of Probability
The probability of a given event is an expression of likelihood or chance of
occurrence of an event. How the number is assigned would depend on the
interpretation of the term probability. There is no general agreement about

1.4
Theorems in Probability
In this module, we shall prove some theorems which help us to evaluate the
probabilities of some complicated events in a rather simple way. In proving these
theorems, we shall follow the axiomatic approach based on the three ax

1.2
Basic Concepts in Probability
Introduction to uncertainty
Every day we have been coming across statements like the ones mentioned
below:
1.
2.
3.
4.
Probably it will rain tonight.
It is quiet likely that there will be a good yield of paddy this year.

2.7
Correlation coefficient and Bivariate Normal Distribution
Meaning of correlation:
In a bivariate distribution we may be interested to find out if there is any correlation
or covariance between the two variables under study. If the change in one variab