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*Claim frequency and claim size are independent
*Claim frequency and claim size are independent
*Monthly claim frequency is Poisson distributed with mean 3
*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.
*The claim size distribution is uniform on [0,1000]


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.
If <math>S</math> is the annual loss, determine the variance of <math>S</math>
 
<ul class="mw-excansopts">
<li>1/2</li>
<li>3/4</li>
<li>1</li>
<li>4/3</li>
<li>5/3</li>
</ul>

Revision as of 01:00, 23 June 2025

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 is uniform on [0,1000]

If [math]S[/math] is the annual loss, determine the variance of [math]S[/math]

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