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