  We study the expected number of real zeros for random linear combinations of
orthogonal polynomials. It is well known that Kac polynomials, spanned by
monomials with i.i.d. Gaussian coefficients, have only $(2/\pi + o(1))\log{n}$
expected real zeros in terms of the degree $n$. On the other hand, if the basis
is given by orthonormal polynomials associated to a finite Borel measure with
compact support on the real line, then random linear combinations have
$n/\sqrt{3} + o(n)$ expected real zeros under mild conditions. We prove that
the latter asymptotic relation holds for all random orthogonal polynomials on
the real line associated with Freud weights, and give local results on the
expected number of real zeros. We also show that the counting measures of
properly scaled zeros of random Freud polynomials converge weakly to the Ullman
distribution.
