2. Let the \( f(\theta) = \frac{n!}{(n - x)!x!}\theta^x (1 - \theta)^{n - x}, x < n \), be the function of \( \theta \in [0,1] \).

Denoted $F(\theta) = \log f(\theta)$, where x and n are the positive, fixed constants. Show that $x/n$ is the unique critical point that is a maximizer of $F$ concerning $\theta$. (15%)