This paper establishes necessary and sufficient conditions for existence, uniqueness and global optimality of the Linear Quadratic Coupled Delay Compensator (LQCDC) which is designed to circumvent the detrimental effects of randomly varying delays from sensor to controller and from controller to actuator as well as the time skew caused by missynchronization of sensor and controller sampling instants. These conditions are derived on the basis of the concepts of stabilizability, detectability and compensatability in the mean square sense. In the absence of random delays from sensor to controller and from controller to actuator, it has been shown that LQCDC problems reduce to the classical Linear Quadratic Gaussian (LQG).