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