Under which condition can a train increase speed when the cab signal indicator changes to a more favorable indication?

The correct choice emphasizes that a train is permitted to increase its speed immediately when the cab signal indicator changes to a more favorable indication, provided there are no contradictions from other signals. This takes into account the operational rules that govern train movements, which are designed for safety and efficiency.

When the cab signal indicates a more favorable condition, it signals the engineer that it is safe to increase speed. However, it is crucial that no other signals provide conflicting information. This rule ensures that the engineer can respond promptly to favorable conditions and maintain the flow of traffic while also upholding safety protocols.

In addition to this, the other choices do not align with the conditions under which speed can be increased as specified by the LIRR Operating Rule Book. For instance, waiting for confirmation from the block operator or checking that the entire length of the train has cleared before increasing speed would unnecessarily delay operations when the cab signal itself already indicates that it is safe to proceed.