Red marrow is not mainly composed of fat cells. Instead, red marrow is responsible for producing red blood cells, white blood cells, and platelets. It is a highly cellular tissue that is found in the spongy bone of certain bones in the body, such as the hip bones, ribs, and sternum. The red marrow contains hematopoietic stem cells, which are responsible for the production of blood cells. Therefore, the given statement is false.