Sensitivity analysis: It is sometimes useful to express the parameters a and b in a beta distribution in terms of 0 = a/(a+b) and n0 = a+b, so that a = 0n0 and b = (1 0)n0. Reconsidering the sample survey data in Exercise 3.1, for each combination of 0 {0.1, 0.2, . . . , 0.9} and n0 {1, 2, 8, 16, 32} find the corresponding a, b values and compute Pr( >0.5| Yi = 57) using a beta(a, b) prior distribution for . Display the results with a contour plot, and discuss how the plot could be used to explain to someone whether or not they should believe that > 0.5, based on the data that 100 Yi = 57.