L
Leila
Member
Can anyone tell me why the answer to question 1.8 in the notes uses 0.95 to the power 25? I thought it would be nPx i.e. e-integral of 0.5 between 0 and 25.
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Question 1.8
Leila,
Your idea would also work but you have confused q and mu. We are being told that q = 0.05 every year for the next 25 years. This is equivalent to a constant force of mortality of -ln (1-0.05) = 0.05129. If we integrate a constant over 25 years we get -ln (1-0.05) X 25. Taking your suggestion of doing e to the minus this, we get exp {-(-ln (1-0.05) X 25)} which is 0.95^25 as required. All round the houses though, orig solution is much nicer - to be employed after 25 years we need to not leave next year (prob 0.95) AND (times) not leave the year after (prob 0.95) AND (times) etc. etc. = 0.95 ^25
Happy Xmas
John
Leila,
Your idea would also work but you have confused q and mu. We are being told that q = 0.05 every year for the next 25 years. This is equivalent to a constant force of mortality of -ln (1-0.05) = 0.05129. If we integrate a constant over 25 years we get -ln (1-0.05) X 25. Taking your suggestion of doing e to the minus this, we get exp {-(-ln (1-0.05) X 25)} which is 0.95^25 as required. All round the houses though, orig solution is much nicer - to be employed after 25 years we need to not leave next year (prob 0.95) AND (times) not leave the year after (prob 0.95) AND (times) etc. etc. = 0.95 ^25
Happy Xmas
John
L
Leila
Member
Thank you John - I had a feeling I might be doing something silly!
TV is so rubbish on Christmas day I was driven to study!
Leila
TV is so rubbish on Christmas day I was driven to study!
Leila