A time-domain method of analysis is presented for the determination of the output mean square values of time-in variant linear systems when subjected to stationary random inputs. Starting with the system unit impulse response function, the system autocorrelation function is derived and a convolution integral theorem for autocorrelation functions is used to give a precise formulation for the output mean square values requiring just a small number of matrix operations. Standard results for a range of input autocorrelation functions are tabulated.