Probability of dying between 1/2 years

[shineon]

What is the formula for calculating that probability that (x) will die between ages x 1/2 and (x+1)1/2? For example, given q70 = 0.04 and q71 = .05 , what is the probability that (70) will die bettwen ages 70 1/2 and 71 1/2 (assuming deaths are uniformly distributed will each year of age). I can't remember how to set this up. Thanks!

[NoMoreExams]

Originally Posted by shineon

What is the formula for calculating that probability that (x) will die between ages x 1/2 and (x+1)1/2? For example, given q70 = 0.04 and q71 = .05 , what is the probability that (70) will die bettwen ages 70 1/2 and 71 1/2 (assuming deaths are uniformly distributed will each year of age). I can't remember how to set this up. Thanks!

Look for formulas here: http://www.actuarialoutpost.com/actu...ad.php?t=92253

But basically you want, in your example

q_{70.5} = {1/2}_q_{70.5} + {1/2}_p_{70.5} * {1/2}_q_{71}

You know that {s}_q_{x} = s*q_{x} for UDD

Basically the logic for my above formula is the prob. that a 70.5 year old will die in the next year is that he will either die in the next 1/2 year or he will survive that half year and die half a year later.

Make sense?

[shineon]

Hmm I see what you mean, but as far as actually calulating it, how can you if you don't know what q70.5 is? And do you have to add to that the probability that he will live to 70.5 in the first place, ie 1/2p70? (I can't look on that site because I'm not a member...)

[NoMoreExams]

Originally Posted by shineon

Hmm I see what you mean, but as far as actually calulating it, how can you if you don't know what q70.5 is? And do you have to add to that the probability that he will live to 70.5 in the first place, ie 1/2p70? (I can't look on that site because I'm not a member...)

1) Well for UDD, {s}_q_{x+t} = s*q_{x} / (1 - t*q_{x})

2) I misread your problem, I thought you were asking for the prob. that a 70.5 year old will die in the next year.

Your question of "what is the probability that (70) will die bettwen ages 70 1/2 and 71 1/2"

Can be written as {1/2|1}_q_{70} and you can use what you know for {t|u}_q_{x} to rewrite it and then solve it the way I said above.

[shineon]

That makes a lot more sense ... thanks for your help!