Jury selection began Monday for a Florida woman with a long history of mental illness charged with killing her teenage son and daughter. Julie Schenecker's lawyers hope to convince jurors she was so psychotic she did not know what she was doing when she shot her daughter, Calyx, 16, and her son, Beau, 13, in January 2011. Police found Calyx's body upstairs in the family home in New Tampa and Beau in the family minivan, his body still fastened by a seatbelt, while their mother was lying on the patio in a bathrobe. Whatever the outcome of the trial, Schenecker could spend the rest of her life in confinement, either in prison or in a secure psychiatric facility. The Hillsborough County State Attorney's Office announced last month that the death penalty is off the table because of Schenecker's psychiatric history. Schenecker, 53, had been diagnosed with bipolar disorder and had been on medication for a long time. Her husband, an Army colonel, filed for divorce after the killings. The trial is expected to take three weeks. Jury selection could last for several days as prosecutors and defense lawyers try to find a panel of people who have not formed opinions on the heavily publicized killings.