**Saralees Nadarajah and Samuel Kotz**

Department of Statistics, University of Nebraska, Lincoln, NE 68583, USA

Department of Engineering Management and Systems Engineering,
The George Washington University, Washington, D.C. 20052, USA.

*Received: 27 January 2005 / Accepted: 13 June 2005 / Published: 14 June 2005*

**Abstract:**
The exact distribution of the linear combination α X + β Y is derived when X and Y
are exponential and gamma random variables distributed independently of each other.
A measure of entropy of the linear combination is investigated.
We also provide computer programs for generating tabulations of the
percentage points associated with the linear combination.
The work is motivated by examples in automation, control, fuzzy sets,
neurocomputing and other areas of computer science.

**Keywords:**
entropy; exponential distribution; gamma distribution; linear combinations of random variables.

**MSC 2000 codes:** 33C90, 62E99.

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