At the 2006 International Conference on Biomedical Engineering, researchers presented an unsupervised learning technique for segmenting skin images. The method employed various forms of a beta distribution, one of which was symmetric. The parameters of a symmetric beta distribution are equal, i.e., α = β. Consider the random variable Y = proportion of pixel shift changes in a skin image following treatment and assume Y follows a symmetric beta distribution.

a. Find E (Y) and interpret the result.

b. Show that the variance of this beta distribution is 1/[4(2α + 1)].