Consider the quadratic optimal control problems for scalar linear stochastic systems with two white coefficients. The influence of an incorrect covariance of the coefficients on the stability of the closed-loop systems is analysed by elementary methods. The set of the true covariance of the coefficients in the systems stabilized by the optimal control designed on a nominal covariance is obtained. It is shown that this set is classified into several patterns according to the parameters of the systems and the weighting coefficient in the performance index and that the particular control gains stabilize the systems with large uncertainty.