A 3-year-old female child with repeated admissions as bleeding tendency in a form of spontaneous ecchymosis and bleeding through the nose and urine

 A 3-year-old female child with repeated admissions as bleeding tendency in a form of spontaneous ecchymosis and bleeding through the nose and urine. She had another daughter who died because of similar undiagnosed illness. The mother is a staff nurse and she is highly concerned about her child illness. Lab investigations usually show»l either PT and/or PTT prolongation with normal platelets, which usually normalized after empiric vitamin K administration. The fatherIs a petrol engineer and never seen accompanying the family. Of the following, the MOST helpful investigation is