1) You need a @synthesize call in the implementation.
Code:
@synthesize myNSMutableArray;
2) use "self." to use the setter/getters produced by the parameters.
Code:
self.myNSMutableArray = [[NSMutableArray alloc] initWithObjects:@"object1.png", @"object2.png", @"object3.png", nil];
[self.myNSMutableArray replaceObjectAtIndex:0 withObject: @"newObject.png"];
Without the "self." you are changing the iVar directly.