Private First Class Alexander was a member of the 38th Field Artillery Battalion, 2nd Infantry Division. He was seriously wounded by the enemy in South Korea on 5 September 1950 and returned to duty later that day. He was taken Prisoner of War while fighting the enemy along the Chongchon River near Kunu-ri, North Korea, on 30 November 1950 and died while a prisoner on 21 February 1951.

Alexander was awarded the Purple Heart with Oak Leaf Cluster, the Prisoner of War Medal, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.