Handbook of Probability (Wiley Handbooks in Applied Statistics) by Florescu Ionut & Tudor Ciprian A

Author:Florescu, Ionut & Tudor, Ciprian A. [Florescu, Ionut]
Language: eng
Format: epub
Publisher: Wiley
Published: 2013-10-28T00:00:00+00:00

We will treat separately the discrete and continuous random vectors.

7.3.3 Discrete Random Vectors

Definition 7.8 We will say that a random vector is discrete if X(Ω) is a finite or countable subset of .

In the single-variable case, the probability function of a discrete random variable X assigns nonzero probabilities to a countable number of distinct values of X such that the sum of the probabilities is equal to 1. Similarly, in the bivariate case (two-dimensional random vector) the joint probability function p(x, y) assigns nonzero probabilities to only a countable number of pairs of values (x, y). Further, the nonzero probabilities must sum to 1.

Remark 7.9 In this case the law of X = (X1, X2, …, XN) is completely determined by the set X(Ω) and the probabilities

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.