This randomized clinical trial aims to (a) test the causal relationship between PA and AD-associated cognitive function for persons with a family history of AD (FH+), (b) determine the moderating role of apolipoprotein epsilon 4 (APOE4) carrier status on cognition, and (c) assess cerebral structure, cerebral function, and putative biomarkers as mediators of the effects of PA on cognition. Here, APOE is linked to Alzheimer disease.