So, either Bill O'Reilly is either on to something profound or he simply doesn't understand averages.  Methinks it's the latter. It's actually a pretty common problem -- people not understanding life expectancy -- it's just that O'Reilly boffs it in such spectacular form! Mathematical expectation is a fancy term for taking an average. You know, sum up the values and divide by the number of cases? In the case of life expectancy, the thing that we're averaging over is the number of years lived by members of a well-defined population. Mechanistically, when we calculate the life expectancy at age $x$ we take all the person-years still to be lived by this group of people and divide by the number who started at age $x$.  The United States has ten times the number of deaths from accidents, etc. as Canada, but it also has ten times the number of people starting at age zero. Oops. I also love the fact that he seems to be attributing the differences in life expectancy between Canada and the United States not to differences in our health care systems but in societal pathologies like more accidents and crime in the United States!