What is 'e' ?

[sahildh]

Well I have gone through the study material many times and as far as I have been thorough with my reading I never encountered the definition of 'e'. I came across many sums where we had to find the value of 'e' and also encountered 'e' in sums where interest rates are zero.
If someone could just really brief me out what is this 'e' both in discrete and continuous form along with the definition and also the formula; will really help me a lot. Also what is its general meaning and where is it used.
This much help would mean a lot.
Thank you.

 

[sahildh]

Anyone, please ?

 

[Julie Lewis]

https://en.wikipedia.org/wiki/E_(mathematical_constant)

 

[sahildh]

https://en.wikipedia.org/wiki/E_(mathematical_constant)

I meant the term
\[e_{x}\] \[e_{[x]}\]
used in relation to mortality.

 

[Julie Lewis]

Ah. That wasn't clear from your original post. It's the expected value of the curtate future lifetime random variable Kx. The expected value of the complete future lifetime random variable Tx is denoted by e_x with a circle above the e. Kx is discrete and Tx is continuous, so you can work out their expected values in the same way as you would for other discrete/continuous random variables.

There are other handy formulae too: E(Kx) = sum from k=1 to infinity of kpx, E(Tx) = integral from t=0 to infinity of tpx dt

 

[sahildh]

Ah. That wasn't clear from your original post. It's the expected value of the curtate future lifetime random variable Kx. The expected value of the complete future lifetime random variable Tx is denoted by e_x with a circle above the e. Kx is discrete and Tx is continuous, so you can work out their expected values in the same way as you would for other discrete/continuous random variables.

There are other handy formulae too: E(Kx) = sum from k=1 to infinity of kpx, E(Tx) = integral from t=0 to infinity of tpx dt

Thanks a lot. Cleared most of my doubts regarding this.