On the Distribution of a Product of Two Random Variables

On the Distribution of a Product of Two Random Variables

Active / Technical Report | Accession Number: AD0736166 |

Abstract:

Let WUV where U and V are independent random variables. It is shown that if V is distributed according to the non-central Chi-square distribution, then W is distributed according to the Chi-square distribution if and only if U1 with probability 1. If V is normally distributed, it is shown that W is normally distributed if and only if the distribution of U is a two-point distribution.

Author(s):

Alam, Khursheed

Author Organization(s):

CLEMSON UNIV SC DEPT OF MATHEMATICAL SCIENCES

Pagination:

0014

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:

Approved For Public Release

Distribution Statement:

Approved For Public Release; Distribution Is Unlimited.

RECORD

Collection: TR

Identifying Numbers

Report Number(s):

TR-76

Contract/Grant Number(s):

N00014-71-A-0339-0002

Project Number(s):

NR-042-271

Monitor Series:

ONR

Subject Terms

Joint Capability Areas:

JCA_1.2_Force Preparation; JCA_1_Force Support; JCA_1.2.3_Educating

Communities of Interest:

No COI(s) Identified

Descriptor(s):

*STATISTICAL DISTRIBUTIONS, MULTIVARIATE ANALYSIS, STATISTICAL TESTS, THEOREMS, RANDOM VARIABLES, PROBABILITY DENSITY FUNCTIONS

Field(s)/Group(s):

Statistics and Probability

Keyword(s):

CHI SQUARE DENSITY FUNCTIONS, DEGREES OF FREEDOM

Report Date:

1971 Sep 01