This paper studies the stability of linear systems with uncertain parameters in the state matrix. Instead of arguing for the worst case like in the classical robust stability methods, we make use of the statistical information on these uncertain parameters, which can be obtained statistically from manufacturing data. Hence, this paper follows the idea of probabilistic robust control and investigates the stability of linear systems with random parameters of known distributions. A sufficient condition for the asymptotic stability in moments is obtained using the generalized Polynomial Chaos expansion theory. Furthermore, to gain more insights on the effects of the random parameters on stability, a special case of uniform distribution is discussed. Finally, the paper concludes with illustrative examples and remarks on future work.