proof given in chapter 9 on page 7 of study material.

[Mohit Gulati]

in this proof they have written nPxx = 1 - nQxx can anybody explain how

nPxx = 1 - nQxx

nPxx should be equal to 1 - (npx*nqx + nqx*npx + nqx*nqx)

 

[Muppet]

Suggest you check back at the summary on page 38 of Chapter 8.
nqxx is the probability that at least one of the lives dies, not that they both die.

 

[Mohit Gulati]

Suggest you check back at the summary on page 38 of Chapter 8.
nqxx is the probability that at least one of the lives dies, not that they both die.

but the point arise that how come they replace
nPxx with 1 - nQxx
is there any way to prove that
npxx = 1 - nqxx

npxx means at least one of the life die
for example if we have two policy holders named x and y of same age and same mortality
so npxx will include the following cases

xdies*y survives + y dies* x survives + x dies * y dies

 

[Muppet]

sorry I might be being dumb - but your equation is right too. The one they use is simply right by definition - no need for a mathematical proof. npxx means they both survive. If they don't, one must have died, and this is what nqxx is defined to be. If you put a bar over the lives it means both have died..

 

[Mohit Gulati]

so what i can see here is they have given a complete notation
of nqxx = (npx*nqx + nqx*npx + nqx*nqx)
since nqxx means at least one dies

and (npx*nqx + nqx*npx + nqx*nqx) also means at least one dies

which makes this now

nqxx + npxx = 1
and that is why npxx = 1 - nqxx