exercise:Ef20ccd421: Difference between revisions
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(Created page with "Scientists are searching for a vaccine for a disease. You are given: (i) <math>\quad 100,000</math> lives age <math>x</math> are exposed to the disease (ii) Future lifetimes are independent, except that the vaccine, if available, will be given to all at the end of year 1 (iii) The probability that the vaccine will be available is 0.2 (iv) For each life during year <math>1, q_{x}=0.02</math> (v) For each life during year 2, <math>q_{x+1}=0.01</math> if the vaccine ha...") |
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Scientists are searching for a vaccine for a disease. You are given: | Scientists are searching for a vaccine for a disease. You are given: | ||
(i) | (i) 100,000 lives age <math>x</math> are exposed to the disease | ||
(ii) Future lifetimes are independent, except that the vaccine, if available, will be given to all at the end of year 1 | (ii) Future lifetimes are independent, except that the vaccine, if available, will be given to all at the end of year 1 | ||
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<ul class="mw-excansopts"><li>100</li><li> 200</li><li> 300</li><li> 400</li><li> 500</li></ul> | <ul class="mw-excansopts"><li>100</li><li> 200</li><li> 300</li><li> 400</li><li> 500</li></ul> | ||
{{soacopyright|2024}} | |||
Latest revision as of 01:26, 18 January 2024
Scientists are searching for a vaccine for a disease. You are given:
(i) 100,000 lives age [math]x[/math] are exposed to the disease
(ii) Future lifetimes are independent, except that the vaccine, if available, will be given to all at the end of year 1
(iii) The probability that the vaccine will be available is 0.2
(iv) For each life during year [math]1, q_{x}=0.02[/math]
(v) For each life during year 2, [math]q_{x+1}=0.01[/math] if the vaccine has been given, and [math]q_{x+1}=0.02[/math] if it has not been given
Calculate the standard deviation of the number of survivors at the end of year 2.
- 100
- 200
- 300
- 400
- 500
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.