A portfolio of policies has the following properties:

• Claim frequency is Poisson distributed with unknown mean [math]\lambda [/math] varying from policy to policy.
• The mean [math]\lambda [/math] is distributed among the risks in the portfolio according to a gamma distribution.
• The expected claim frequency for a randomly selected policy is 2.
• The probability of a claim frequency observation equaling zero for a randomly selected risk is 27/125.

Determine the variance of [math]\lambda [/math].

1. 1
2. 4/3
3. 2
4. 3
5. 27/4