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You are given the following about a risk:
You are given the following:


*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
*Claim size is uniformly distributed on [a,b]
*The claim size distribution is uniform on [0,1000]


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).
If <math>S</math> is the annual loss, determine the variance of <math>S</math>


<ul class="mw-excansopts">
<ul class="mw-excansopts">
<li>1/2</li>
  <li>8,000,000</li>
<li>3/4</li>
  <li>10,500,000</li>
<li>1</li>
  <li>11,000,000</li>
<li>4/3</li>
  <li>12,000,000</li>
<li>5/3</li>
  <li>13,000,000</li>
</ul>
</ul>

Latest revision as of 01:28, 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]

  • 8,000,000
  • 10,500,000
  • 11,000,000
  • 12,000,000
  • 13,000,000