Summary: In networked control systems, random delays and packet dropouts are inevitable during data transmissions due to the limited communication capacity. The phenomena of random delays and packet dropouts of both sides from a sensor to an estimator and from a controller to an actuator are modeled via employing two groups of Bernoulli random variables. By defining some new variables, the original system with random delays and packet dropouts is equivalently transformed into a stochastic parameterized system. The optimal linear filter, predictor and smoother in the linear minimum variance sense are presented via the orthogonality projection approach. They depend on the probabilities of the stochastic parameters. The solutions to the optimal linear estimators are given by three equations including a Riccati, a Lyapunov and a simple difference. The stability of the proposed estimators is analyzed. At last, a sufficient condition for the existence of the steady-state estimators is given for time-invariant systems. Two examples are provided to verify the effectiveness of the proposed algorithms.