The scene of the crime is a dimly lit study inside a grand, Victorian-era mansion. There's a large oak desk at the center of the room, and the deceased, Lord Barrington, lies slumped over it with a gunshot wound to the chest. A shattered windowpane hints at the possible point of entry for the assailant. The three main suspects are: 1) Lady Barrington, the victim's wife, who had increasing disputes with her husband; 2) Randall, the family's loyal butler, who recently discovered he was going to be replaced; and 3) Edgar, a distant cousin, who expected a large inheritance if Lord Barrington passed away. My plan to investigate the case includes: interviewing each suspect about their whereabouts during the crime; examining the broken window for any fingerprints or signs of forced entry; and analyzing the murder weapon, a pistol, to trace its ownership and look for any additional evidence like partial fingerprints or other traces left by the culprit.
Imagine you are a detective trying to solve a murder mystery in a fictional Victorian-era town. Describe the scene of the crime, the main suspects, and your plan to investigate the case.