Consider a commodity with constant volatility $\sigma$ and an expected growth rate that is a function solely of time. Show that, in the traditional risk-neutral world,
$$\ln S_T \sim \phi\left[\ln F(T)-\frac{1}{2} \sigma^2 T, \sigma^2 T\right]$$
where $S_T$ is the value of the commodity at time $T, F(t)$ is the futures price at time 0 for a contract maturing at time $t$, and $\phi(m, v)$ is a normal distribution with mean $m$ and variance $t$.