Unit : 1.2 Convergence and Limit Theorems :

 Unit : 1.2 : Convergence and Limit Theorems

Definition of convergence of sequence of random variables 

                        a) in probability  

                        b) in distribution  

                        c) in quadratic mean 

   Convergence in probability: 




***


* Convergence in Quadratic Mean : 

* Weak Law of Large Numbers (WLLN)
                                    
***


***

Central Limit Theorem : (CLT)

***






Comments

Post a Comment

Popular posts from this blog

Unit 1 : Multiple Regression , Multiple Correlation and Partial Correlation 1.1: Multiple Linear Regression (for trivariate data)

Image
  Unit 2 : Multiple Regression , Multiple Correlation and Partial Correlation  Unit 2.1 Multiple Linear Regression  (for tri variate data)      Some statistical methods serve as forecasting or estimation techniques. One of such is regression analysis. We have learnt concept of linear regression and correlation with respect to two variables. It is called as simple correlation and simple regression.      In practice, the variable under study is influenced by two or more variables. For example: national income based on several variables such as agricultural yield, industrial production, import, export production of minerals, marine wealth etc.       For accuracy in prediction it is inevitable to include all interrelated  variables in the regression model. Among such variables, whose value is to be predicted  is called as dependent variable or  response variable and remaining variables are treated as independen...
Read more
Image
  RELIABILITY THEORY INTRODUCTION:  ©                In day-to-day life we come across several types of machines, equipment, systems such as radio set, T. V. set, vehicle, electric bulb, computer, music system etc. We always ask questions to manufacture that how long the machine will work without any trouble. What is the guarantee period of the item? Answers to such questions are based on the life time of the components of machine as well as the entire assembly. A reliability theory deals with extensive study of life time of components and machines. This is one of the important branch having wide applications in the manufacturing process.                    Reliability theory is concerned with determining a probability that, a system of several components is functioning i.e. working at a specified time ‘t’. The se...
Read more

Time Series

Image
                                                                                  Unit... 1.1 Time series There is nothing constant in the universe All ebb and flow, and every shape that’s born Bears in its womb the seeds of change.                                    - Ovid introduction:©                                 The world is dynamic. There is nothing stable or constant in world. Changes are taking place at every moment of time. It is rightly sai...
Read more