Two phases of the study will be conducted. The Phase I will establish the maximum tolerated dose of carboplatin and 5'azacytidine in a rolling 6 design. 5'azacytidine will be administered on Days 1-7 followed by Carboplatin on Day 15. The initial dose level will be 5'Azacytidine 75mg/m2/day for 7 days with Carboplatin administered on Day 15 at AUC (Area under curve) 4. Carboplatin will be dose escalated to a maximum of AUC 6, or de-escalated to AUC 3. The Phase Ib will be an ependymoma specific expansion cohort at the established MTD (maximum tolerated dose), to determine the feasibility and initial efficacy of the combination of carboplatin and 5'azacytidine in patients with recurrent/refractory posterior fossa and supratentorial ependymoma.