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Let $z_u,z_d$ be the state-price-density values at the higher and lower risky payoff. Pricing the two assets givesSolving yieldsBoth values are positive, and the two independent equations make the solution unique. The payoff matrix has nonzero determinant, so this is a complete two-state market. The actual Arrow state prices, including physical probabilities, are $q_u=5/9$ and $q_d=5/18$. Their sum is $5/6$, the discount factor. Normalizing gives risk-neutral probabilities $2/3,1/3$. Thus $Z$ itself is not a probability density of mean one: its mean is $5/6$ because the riskless asset earns interest.