Transcription of Random Variables and Probability Distributions
{{id}} {{{paragraph}}}
Example: confidence
Random Variables and Probability Distributions
ARandom Variablesand Probability Distribution Functions and Random The Multivariate Normal Distribution Functions and ExpectationThe distribution functionFof a Random variableXis defined byF(x)=P[X x]( )for all realx. The following properties are direct consequences of ( ) nondecreasing, ,F(x) F(y)ifx right continuous , ,F(y) F(x)asy (x) 1andF(y) 0asx andy , , any function that satisfies properties 1 3 is the distribution function ofsome Random of the commonly encountered distribution functionsFcan be expressedeither asF(x)= x f(y)dy( )orF(x)= j:xj xp(xj),( )where{x0,x1,x2,..}is a finite or countably infinite set. In the case ( )weshallsay that the Random variableXiscontinuous. The functionfis called theprobabilitydensity function(pdf) ofXand can be found from the relationf(x)=F (x). Springer International Publishing Switzerland Brockwell, Davis,Introduction to Time Series and Forecasting,Springer Texts in Statistics, DOI A Random Variables and Probability DistributionsIn case ( ), the possible values ofXare restricted to the set{x0,x1.}
356 Appendix A Random Variables and Probability Distributions whereW 1 isacontinuous random variable. Ifthedistribution of W 1 isexponential with parameter 1, then the distribution function of W is F(x) = 0, if x < , 1 2 + 1 2 1 −e −x = 1 − 1 2 e , if x ≥ 0. This distribution function is neither continuous (since it has a discontinuity at x = 0) nor discrete (since it increases ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: