Australian crab data: The files bluecrab. dat and orangecrab. dat contain measurements of body depth (Y1) and rear width (Y2), in millimeters, made on 50 male crabs from each of two species, blue and orange. We will model these data using a bivariate normal distribution.

a) For each of the two species, obtain posterior distributions of the population mean θ and covariance matrix Σ as follows: Using the semiconjugate prior distributions for θ and Σ, set µ0 equal to the sample mean of the data, Λ0 and S0 equal to the sample covariance matrix and ν0 = 4. Obtain 10,000 posterior samples of θ