The fifth of twelve children born to a prominent Shreveport businessman, Alexander was educated in private elementary and secondary schools. He received his Bachelor of Arts degree from Louisiana State University in Shreveport. He obtained his law degree from Oklahoma City University School of Law where he served on Law Review and Moot Court, both intramural and on the Benton National Moot Court Team. He was a law clerk to Judge Rebecca F. Doherty of the U.S. District Court for the Western District of Louisiana. An appointee of former U.S. President George H.W. Bush, Doherty is based in Lafayette and Opelousas. Himself a former administrative law judge, Alexander has also been in private practice, handling both criminal and civil cases.