The purpose of this paper is to study the random input in a discrete-time linear optimal control system. Since the random input includes the measurement noise and disturbance input, it is often referred as white noise when evaluating a quadratic performance functional. With the random input presented in a system, the state variable is impossible determined precisely at the later time. Due to the existence of noise, the state variable is considered as a random sequence which satisfies the Markov property and could be described by the probability transition matrix. Additional, the mean-value and the covariance matrix of the state give the meaningful information for investigation of the stochastic linear optimal control system. A simple simulation of scalar system is discussed and the graphical optimal solution is represented.