Hi Brajaballav,

I suggest you have a look on usual methods for constructing life tables, which can be seen as multiperiod age-pyramids, or alternatively at courses concerning duration models considering your question is quite "general/global". Concerning your questions about relationships, there are plenty, one that I find interesting is : If you have real positive random variable X, let's take it absolutely continuous  with respect to ν (Lebesgue's measure), then :

\[ \mathbb{E}\left[X\right] =  \int_{0}^{+ \infty} \mathbb{P}\left[X \geq x \right] \mathrm{d}x \]

Best regards, 

Thank you Geoffrey