exercise:A412453a8a: Difference between revisions
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You are given the following | You are given the following: | ||
*Claim frequency and claim | *Claim frequency and claim size are independent | ||
*Monthly claim frequency is Poisson distributed | *Monthly claim frequency is Poisson distributed with mean 3 | ||
* | *The claim size distribution depends on parameters <math>a,b</math>: when <math>a < b </math> the distribution is uniform on <math>[a,b]</math> and when <math>a = b </math> the claim size equals <math>b </math> with probability 1. | ||
If <math>S</math> is | If <math>S</math> is the annual loss, determine the maximum of <math>\operatorname{E}[S^2]/\operatorname{E}[S]^2</math> over all possible values a,b. | ||
< | <ul class="mw-excansopts"> | ||
<li>1/2</li> | <li>1/2</li> | ||
<li>3/4</li> | <li>3/4</li> | ||
| Line 13: | Line 13: | ||
<li>4/3</li> | <li>4/3</li> | ||
<li>5/3</li> | <li>5/3</li> | ||
</ | </ul> | ||
Latest revision as of 21:48, 24 July 2024
You are given the following:
- Claim frequency and claim size are independent
- Monthly claim frequency is Poisson distributed with mean 3
- The claim size distribution depends on parameters [math]a,b[/math]: when [math]a \lt b [/math] the distribution is uniform on [math][a,b][/math] and when [math]a = b [/math] the claim size equals [math]b [/math] with probability 1.
If [math]S[/math] is the annual loss, 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