A statistician is trying to decide on the value of an unknown parameter ϴ, where ϴ is the maximum claim that can occur for a line of business whose claims are uniformly distributed on the interval (0, ϴ). In making the decision, the statistician randomly selects a single loss from the line of business, which takes the value x, and estimates ϴ as ϴ*=kx where k is a constant. The statistician is using a quadratic loss function: that is to say the loss incurred based on their decision is proportional to the squared distance between the true value ϴ and their estimate ϴ*. Find the form of their estimate ϴ* based on the sample outcome x in order to minimize the expected risk.