In fields that require high precision surface height maps, white light interferometry (WLI) has become the standard inspection tool. Because WLI generates two-dimensional height profiles, and standard mechanical devices used with WLI generate only one-dimensional profiles, engineers must estimate the mean height of pixels generated in WLI surface maps. In Optical Engineering (Jan. 2005), German researchers applied Bayesian estimation to solve the problem. A simplified version of the research is stated as follows: Let Y represent the height for a pixel generated by WLI. Assume that Y takes on the value 1 with probability p and the value 0 with probability (1 - p). Also, assume that p has a beta distribution with parameters α = 1 and β = 2. Now let y₁, y₂, y₃, . . . , y_n represent the heights for a sample of n pixels. Using a squared error loss function, find the Bayesian estimate of p if y̅ = .80