Subject and UNIT: Random Process and Linear Algebra: Unit III: Random Processes,,
"If a random process is stationary to all order then the random process is said to be strict sense stationary process."
Definition, Examples
Subject and UNIT: Random Process and Linear Algebra: Unit III: Random Processes,,
A random process is conceptually an extension of a random variable. A random variable is a function of time is called a random process. New problems in various branches of Engineering and Science, do not fit into the frame work of the classical probability theory. Such problems arouses us to study the processes, that is, phenomena that takes place in time. It is necessary to develop random processes which is a family of random variables that is indexed by a parameter such as time.
Subject and UNIT: Random Process and Linear Algebra: Unit II: Two-Dimensional Random Variables,,
Two dimensional random variables important question with answers
Independent and identically distributed random variables
Subject and UNIT: Random Process and Linear Algebra: Unit II: Two-Dimensional Random Variables,,
The most widely used model for the distribution of a random variable is a normal distribution. Whenever a random experiment is replicated, the random variable that equals the average result over the replicates tends to have a normal distribution as the number of replicates becomes large. De Moivre presented this fundamental result, known as the central limit theorem, in 1733. The central limit theorem says that the probability distribution function of the sum of a large number of random variables approaches a gaussian distribution. Although the theorem is known to apply to some cases of statistically dependent random variables, most applications, and the largest body of knowledge are directed towards statistically independent random variables.
Subject and UNIT: Random Process and Linear Algebra: Unit II: Two-Dimensional Random Variables,,
i. Two functions of two random variables ii. One function of two random variables
Subject and UNIT: Random Process and Linear Algebra: Unit II: Two-Dimensional Random Variables,,
Regression is a mathematical measure of the average relationship between two or more variables in terms of the original limits of the data.
Subject and UNIT: Random Process and Linear Algebra: Unit II: Two-Dimensional Random Variables,,
When two or more random variables are defined on a probability space, it is useful to describe how they vary together, that is, it is useful to measure the relationship between the variables. A common measure of the relationship between two random variables is the covariance. To define the covariance, we need to describe the expected value of a function of two random variables h (x, y). The definition simply extends that used for a function of a single random variable.
Subject and UNIT: Random Process and Linear Algebra: Unit II: Two-Dimensional Random Variables,,
Important Problems under the continuous random variables
Subject and UNIT: Random Process and Linear Algebra: Unit II: Two-Dimensional Random Variables,,
The type of disjoint distributions are explained.
Subject and UNIT: Random Process and Linear Algebra: Unit II: Two-Dimensional Random Variables,,
Various aspects of the theory of single random variable were studied. The random variable was found to be a powerful concept. It enabled many realistic problems to be described in a probabilistic way such that practical measures could be applied to the problem even though it was random.
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
Important Question and Answers
Deviation, Characteristics of Normal Distribution
Subject and UNIT: Random Process and Linear Algebra: Unit I: Probability and Random Variables,,
The Normal Distribution was introduced by the French Mathematician Abraham De Moivre in 1733. Demoivre, who used this distribution to approximate probabilities connected with coin tossing, called if the exponential bell-shaped curve.