Hi Rohin

For a very small h, \( \mu_xh\) can be interpreted as the probability that a newborn who has attained age \(x\) dies between \(x\) and \(x+h\):

\( \mu_xh \approx Pr[x\lt X \le x+ h| X \gt x]\)

You can think of force of mortality as the conditional instantaneous measure of death at \(x\).

With regards to your second question, a good model will **not** always have an increasing force of mortality. The force of mortality in fact decreases in late teenage years/early twenties and this effect is called the "accident hump". This occurs as a result of deaths from car accidents of inexperienced drivers, and drug/alcohol-related deaths. The Balducci assumption for instance exhibits decreasing force of mortality so could possibly be used in a model to explain the "accident hump". After these years, the force of mortality does increase due to individuals becoming older so more likely to die.