exercise:A412453a8a: Difference between revisions
From Stochiki
No edit summary |
No edit summary |
||
| Line 2: | Line 2: | ||
*Claim frequency and claim size are independent | *Claim frequency and claim size are independent | ||
*Monthly claim frequency is Poisson distributed | *Monthly claim frequency is Poisson distributed with mean 3 | ||
*Claim size is uniformly distributed | *Claim size is uniformly distributed on [a,b] | ||
If <math>S</math> is an annual loss for the risk, determine the maximum of <math>\operatorname{E}[S^2]/\operatorname{E}[S]^2</math>. | If <math>S</math> is an annual loss for the risk, determine the maximum of <math>\operatorname{E}[S^2]/\operatorname{E}[S]^2</math> over all possible values (a,b). | ||
<ul class="mw-excansopts"> | <ul class="mw-excansopts"> | ||
Revision as of 21:48, 15 July 2024
You are given the following about a risk:
- Claim frequency and claim size are independent
- Monthly claim frequency is Poisson distributed with mean 3
- Claim size is uniformly distributed on [a,b]
If [math]S[/math] is an annual loss for the risk, determine the maximum of [math]\operatorname{E}[S^2]/\operatorname{E}[S]^2[/math] over all possible values (a,b).
- 1/2
- 3/4
- 1
- 4/3
- 5/3