The first foundation of the mathematical theory of probability was laid in the seventeenth century while dealing with some problems related to the theory of dice in gambling. Since then it has found extensive applications in various branches of science and engineering. The definition of probability is achieved through the study of certain basic concepts in probability theory, which deals with the ......

Consider a sample space S of a random experiment. We shall find out a rule by which each element of S may be associated with a number x or an ordered pair (x, y). Such a rule is called a random variable. So by a random variable we mean a real number connected with the outcome of a random experiment.

Now let us discuss some special theoretical distributions in which variables are distributed according to some definite probability law which can be expressed mathematically.

In a bivariate distribution we may be interested to find our whether there is any correlation between the two variables under study. For example, if the bivariate distribution represents the height and weight of a group of individuals, then they are related. Correlation analysis is the statistical technique used to describe not only the degree of relationship between the variables but also the dir ......

Now we are going to study about a family of random variables. A family of random variables indexed by a parameter (like time,) is known as a stochastic process or a random process. We know that the r.v. X, is by definition, a function of the possible outcomes S, of an experiment. Now a random process is a function of both time and S. When time t is fixed, the random process represents the random v ......

We can characterise processes by means of auto correlation, cross-correlation and covariance functions without any consideration of spectral properties. Both time domain and frequency domain analysis methods exist for analysing Linear systems and Deterministic wave forms. Similarly we have to describe random processes in the frequency domain. The spectral description of a deterministic wave form i ......

The word reliable is commonly used in the same sense as dependable when we say that a component is reliable then it means that it will behave in a manner in which it is expected to, under normal or assumed conditions. When it happens to fail unexpectedly, we accept it as a chance failure. These qualifications (i.e.) the expected behaviour under some stated or assumed conditions along with a certai ......

There are two types of estimates about a population: Point estimate and an Interval estimate. Point estimate a point estimate is a single number that is used to estimate an unknown population parameter. A point estimate is inefficient because it is either right or wrong, hence it is much more useful of it is accompanied by an estimate of error that might be involved. Interval estimate An interval ......

The Arriving pattern of queue has regular or irregular intervals of time. One or more service channels or service stations or service facilities can be assembled in Queueing procedure.