What are the four types of stochastic process?
Based on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and branching processes.
Can values of random variable be repeated?
Continuous random variables can represent any value within a specified range or interval and can take on an infinite number of possible values.
What are the features of multivariate random variable?
In probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value.
How does a stochastic variable help in simulation?
A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. Realizations of these random variables are generated and inserted into a model of the system.
What is the meaning of stochastically?
1 : random specifically : involving a random variable a stochastic process. 2 : involving chance or probability : probabilistic a stochastic model of radiation-induced mutation.
Is the random variable discrete or continuous?
A discrete variable is a variable whose value is obtained by counting. A continuous variable is a variable whose value is obtained by measuring. A random variable is a variable whose value is a numerical outcome of a random phenomenon. A discrete random variable X has a countable number of possible values.
What is continuous random variable?
A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.
Why is multivariate data analysis used?
Multivariate data analysis helps in the reduction and simplification of data as much as possible without losing any important details. As MVA has multiple variables, the variables are grouped and sorted on the basis of their unique features.
What are variables in multivariate analysis?
Multivariate analysis is used to describe analyses of data where there are multiple variables or observations for each unit or individual. • Often times these data are interrelated and statistical methods are needed to fully answer the objectives of our research.
What is significance of stochastic term in economic analysis?
Stochastic properties are the basic determinants of behavior of economic variables. These properties are also important for construction of econometric models, interpretation of the findings and forecasting. So prior to any econometric study time series properties of variables have to be analyzed.
Why do we need stochastic process?
Since stochastic processes provides a method of quantitative study through the mathematical model, it plays an important role in the modern discipline or operations research.
What is an exponential distribution for a continuous random variable?
A continuous random variable X is said to have an exponential distribution with parameter λ, λ > 0, if its probability density function is given by f(x) = {λe − λx, x ⩾ 0 0, x < 0 or, equivalently, if its cdf is given by F(x) = ∫ x − ∞ f(y)dy = {1 − e − λx, x ⩾ 0 0, x < 0
What is an exponential random variable (RV)?
An exponential random variable (RV) is a continuous random variable that has applications in modeling a Poisson process. Poisson processes find extensive applications in tele-traffic modeling and queuing theory.
What is an exponential distribution with parameter λ > 0?
A continuous random variable X is said to have an exponential distribution with parameter λ, λ > 0, if its probability density function is given by The mean of the exponential distribution, E[X], is given by The moment generating function ϕ(t) of the exponential distribution is given by
When does the time until the next arrival become exponentially distributed?
Thus, if we consider the occurrence of an event governed by the exponential distribution as an arrival, then given that no arrival has occurred up to time t, the time until the next arrival is exponentially distributed with mean 1/ λ. In particular, it can be shown, as in Ibe (2005), that