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## Remarks on conditional moments of the free deformed Poisson random variables

### Volume 96 / 2011

Banach Center Publications 96 (2011), 135-145 MSC: Primary 46L53, 46L54; Secondary 60E10. DOI: 10.4064/bc96-0-8

#### Abstract

We will show that the conditional first moment of the free deformed Poisson random variables ($q=0$) corresponding to operators fulfilling the free relation is a linear function of the regression and the conditional variance also is a linear function of the regression. For this purpose we will first demonstrate some properties of the Wick product and then we will concentrate on the free deformed Poisson random variables.

#### Authors

• Wiktor EjsmontMathematical Institute, University of Wrocław
pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
e-mail

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