4. (5 %) Let f(x|θ) be the logistic location pdf

$$f(x|\theta) = \frac{e^{(x-\theta)}}{(1 + e^{(x-\theta)})^2}, -\infty < x < \infty, -\infty < \theta < \infty.$$

Based on one observation, X, find the most powerful size α test of H0: θ = 0 versus H1: θ = 1.