Death Wish

Paul Kersey is an architect living in Manhattan with his wife Joanna and grown daughter Carol Toby. The film begins with scenes of a recent vacation Paul and Joanna had taken to Hawaii. One day, Joanna and Carol are followed home from D'Agostino's by three thugs who invade the apartment by posing as deliverymen. They fatally injure Joanna and sexually assault Carol.
After his wife's funeral in Connecticut during a snowstorm and shortly following his return to work, Paul's boss gives him an extended business vacation, and he flies to Tucson, Arizona to meet a client, Ames Jainchill. While working in Tucson, Paul witnesses a mock gunfight at Old Tucson, a reconstructed Western frontier town used as a movie set. A few days later while he is working late at Ames's offices, Paul is invited to dinner by Ames at Ames's club. It is a gun club. At the gun club, Ames is impressed when Paul shoots with near bulls-eye accuracy. Paul reveals that he was a conscientious objector during the Korean War who served as a combat medic. Paul had been taught to handle firearms at a young age by his father, who was a skilled hunter and shooter, but after his father was killed in a hunting accident Paul decided to forswear the use of firearms for any purpose. After Paul makes substantial improvements to Ames' plans for a residential development, a thoroughly pleased Ames drives Paul back to the Tucson airport, and presents Paul with a gift, which he places into Paul's checked luggage.
Back in Manhattan, Paul learns from his son-in-law that his daughter is severely depressed from the trauma of the assault. Paul visits his daughter, who is now catatonic, at the hospital. Heartbroken, Paul and his son-in-law have his daughter committed to a mental hospital on Long Island for intensive treatment. Later upon his return to Manhattan, he opens his suitcase and discovers that Ames' gift is a nickel-plated .32 Colt Police Positive revolver. He loads the revolver, places it into his overcoat, and takes a late night stroll. Paul encounters a mugger, an ex-convict named Thomas Leroy Marston, who attempts to rob him at gunpoint with a .38 Smith &amp; Wesson Model 36 revolver. Paul then shoots and kills Marston with the revolver Ames had given him.
Shocked that he just killed a human being, Paul runs home and vomits. But motivated by his desire for revenge, he continues to walk the city streets at night looking for violent criminals. The following night, Paul again deliberately walks through the city in order to invite an attack. He guns down three more men who are robbing a defenseless old man in a vacant alley. A few nights later, two muggers see Paul on a subway. They attempt to rob him at knife-point but Paul shoots them both with his revolver.
On another night, Paul sits as bait in a sleazy Times Square coffee shop surrounded by prostitutes and assorted street people. He pays his bill to the cashier, purposely revealing a wallet full of cash. He leaves followed by two thugs who have taken the bait. Yet again a robbery attempt is made. Paul shoots one but the other manages to stab him in his shoulder. As a wounded Paul stumbles off, the one who stabbed him gets away mortally wounded, dying at a hospital.
NYPD Lt. Frank Ochoa investigates the vigilante killings. His department narrows it down to a list to men who have had a family member recently killed by muggers and who are war veterans. The public, meanwhile, is happy that somebody is doing something about crime. Ochoa soon suspects Paul. He is about to make an arrest when the District Attorney intervenes and tells Ochoa to "let him loose" in another city instead. The D.A. and the Police Commissioner do not want the fact to get out that street crime in New York City has dropped dramatically since Paul became a vigilante. And they fear that if he isn't stopped the whole city will explode into anarchy. Ochoa doesn't like the idea, but relents. Ochoa says that he will try to "scare him off."
Paul shoots two more muggers before being wounded by a third mugger with a M1911A1 pistol at a warehouse. His gun is discovered by a young patrolman, Jackson Reilly, who secretly hands it to Ochoa, who tells him to forget that he ever saw it and additionally tells the press that the wounded Paul is just another mugging victim. Hospitalized, Paul is ordered by Ochoa to leave New York, permanently. Ochoa tells Paul to have his company transfer him to another city and, in exchange, Ochoa will dump Paul's Colt revolver in the river. As Ochoa walks out of Paul's hospital room, Paul replies, "By sundown?".
Paul arrives in Chicago Union Station by train. Being greeted by a company representative, he notices a group of hoodlums harassing a young woman. He excuses himself and helps the woman. The hoodlums make obscene gestures, but Paul points his right hand like a gun and smiles, suggesting that his vigilantism will continue.

Question: What type of killings does Frank Ochoa investigate?
Answer: Vigilante