A note about the average number of real roots of a Bernstein polynomial system

We prove that the real roots of normal random homogeneous polynomial systems with n+1n+1 variables and given degrees are, in some sense, equidistributed in the projective space P(Rn+1)P(Rn+1). From this fact we compute the average number of real roots of normal random polynomial systems given in the Bernstein basis.