  In this paper we have explicitly computed the $position-position$ and
$position-momentum$ (Heisenberg) Uncertainty Relations for the model of
relativistic particles with arbitrary spin, proposed by Jackiw and Nair ref.[1]
as a model for Anyon, in a purely quantum mechanical framework. This supports
(via Schwarz inequality) the conjecture that anyons live in a 2-dimensional
\textit{noncommutative} space. We have computed the non-trivial uncertainty
relation between anyon coordinates, ${\sqrt{\Delta x^2\Delta
y^2}}=\hbar\bar{\Theta}_{xy}$, using the recently constructed anyon wave
function ref.[6], in the framework of ref.[7]. We also compute the Heisenberg
(position-momentum) uncertainty relation for anyons. Lastly we show that the
identical \textit{formalism} when applied to electrons, yield a trivial
position uncertainty relation, consistent with their living in a 3-dimensional
commutative space.
