Hi!

I found a genetic anomaly in his blood sample.
Anomaly : not normal.

The judge gave an equivocal decision which was not biased to any of the two part.
equivocal: neutral, uncertain.

The lecture on physics given by the professor was completely lucid.
lucid: transparent, to the point, clear.

precipitate: to bring down.

The customer care executive  was able to assuage the angry customer.
assuage: to satisfy someone, to mollify someone, to pacify.

The theories that are mentioned showed their erudite beginnings.
erudite: profound knowledge.

 His prodigal habit lead his father to remove his name from his will.
prodigal: wasteful, spending resources recklessly.