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

Discussion in 'CT5' started by Mohit Gulati, Sep 4, 2018.

  1. Mohit Gulati

    Mohit Gulati Active Member

    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)
     
  2. Muppet

    Muppet Member

    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.
     
  3. Mohit Gulati

    Mohit Gulati Active Member

    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
     
  4. Muppet

    Muppet Member

    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..
     
  5. Mohit Gulati

    Mohit Gulati Active Member

    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
     

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