The members of a police force established under authority of RCW 28B.10.550, when appointed and duly sworn:

(1) Shall be peace officers of the state and have such police powers as are vested in sheriffs and peace officers generally under the laws of this state; and

(2) May exercise such powers upon state lands devoted mainly to the educational or research activities of the institution to which they were appointed; and

(3) Shall have power to pursue and arrest beyond the limits of such state lands, if necessary, all or any violators of the rules or regulations herein provided for.