exercise:D517496346: Difference between revisions
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<li><math>\frac{1}{18}(1 − e^{−2/3} − e^{−1/2} + e^{−7/6} )</math></li> | <li><math>\frac{1}{18}(1 − e^{−2/3} − e^{−1/2} + e^{−7/6} )</math></li> | ||
<li><math>\frac{1}{18} e^{−7/6} </math></li> | <li><math>\frac{1}{18} e^{−7/6} </math></li> | ||
<li><math> | <li><math>1 − e^{−2/3} − e^{−1/2} + e^{−7/6}</math></li> | ||
<li><math>1 − e^{−2/3} − e^{−1/2} + e^{−1/3} </math></li> | <li><math>1 − e^{−2/3} − e^{−1/2} + e^{−1/3} </math></li> | ||
<li><math>1 − \frac{1}{3}e^{−2/3} − \frac{1}{6}e^{−1/2} + \frac{1}{18}e^{−7/6} | <li><math>1 − \frac{1}{3}e^{−2/3} − \frac{1}{6}e^{−1/2} + \frac{1}{18}e^{−7/6} | ||
Latest revision as of 14:24, 2 May 2023
The waiting time for the first claim from a good driver and the waiting time for the first claim from a bad driver are independent and follow exponential distributions with means 6 years and 3 years, respectively.
Calculate the probability that the first claim from a good driver will be filed within 3 years and the first claim from a bad driver will be filed within 2 years.
- [math]\frac{1}{18}(1 − e^{−2/3} − e^{−1/2} + e^{−7/6} )[/math]
- [math]\frac{1}{18} e^{−7/6} [/math]
- [math]1 − e^{−2/3} − e^{−1/2} + e^{−7/6}[/math]
- [math]1 − e^{−2/3} − e^{−1/2} + e^{−1/3} [/math]
- [math]1 − \frac{1}{3}e^{−2/3} − \frac{1}{6}e^{−1/2} + \frac{1}{18}e^{−7/6} [/math]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.