Why _{0}p_{x}=1?

I'll be grateful for help :)

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- Apr 22nd 2009, 11:39 AMLenaWhy probability of living 0 years equals 1?
Why _{0}p_{x}=1?

I'll be grateful for help :) - Apr 22nd 2009, 01:58 PMmr fantastic
- Apr 22nd 2009, 10:58 PMmatheagle
I'm biting my tongue right now.

I have so many light bulb questions I want to ask. - Apr 23rd 2009, 09:28 AMLena
Oh of course, I thought it would be enough.

It is :

$\displaystyle _{0}p_{[x]+s}=1$

This is a part of first element of sum:

$\displaystyle \sum_{n=0}^{\infty}\pi_{s+n}v^{n}_{n}p_{[x]+s} $ - Apr 23rd 2009, 02:22 PMmatheagle
Thanks, that clears up everything.

- Apr 23rd 2009, 02:42 PMUnenlightened
- Apr 24th 2009, 08:54 AMLena
$\displaystyle _{n}p_{[x]+s}$ is the conditional probability that a person of x will live at least n years, on condition that he will live s years before.

Thanks mr fantastic for info about latex tags. - Apr 24th 2009, 09:05 AMUnenlightened
So what you're asking in this case is...

Given that a person aged 'x' has lived for the previous 's' years, what are the chances they will live at least 0 more years?

That is, 1 - P(they will not live for more than 0 years)..? has to equal 1..

Unless the person in question died while they were filling in the survey. - Apr 24th 2009, 09:34 AMLena
Yes, thats what I'm asking about.

Well maybe its about it, it would be

$\displaystyle _{0}p_{[x]+s}=1-_{0}q_{[x]+s}$

where $\displaystyle _{0}q_{[x]+s}$ is the conditional probability that a person of x will die in a period of '0' years, on condition that first will live for s years. But how much then is $\displaystyle _{0}q_{[x]+s}$ :confused: - Apr 24th 2009, 09:44 AMCaptainBlack
- Apr 24th 2009, 12:59 PMLena
x is age of the person, in a moment of concluding an isurance contract.

- Apr 24th 2009, 01:16 PMCaptainBlack
- Apr 25th 2009, 02:43 AMLena
The person of age 'x' first has to live 's' years, and then what is probability that he will live '0' years. It has to equal 1.

- Apr 25th 2009, 06:14 AMUnenlightened
Suppose you're 57, (which is x in this case ), wanting a pension for when you're 65.

So s in this case would be 8. (Because they're not going to pay that particular pension scheme if you die before you 65th birthday).

The insurance company want to know how likely you are to live for at least n years after your 65th birthday, so they know how much pension you're likely to collect in total before you kick the bucket.

In this case, n is 0.

So the question is: assuming you, 57, live the 8 years until your 65th birthday, what is the probability that you live for at least 0 years after your 65th birthday.

Or the probability that you die within 0 years of your 65th birthday.

(0 years in this case means no time whatsoever. 0 years, 0 months, 0 days, 0 hours, 0 seconds.)

As far as I know.

I could be wrong.

It has happened before.