Mixture models: After a posterior analysis on data from a population of squash plants, it was determined that the total vegetable weight of a given plant could be modeled with the following distribution:

p(y|, 2 ) = .31dnorm(y, , ) + .46dnorm(21, 2) + .23dnorm(y, 31, 3)

where the posterior distributions of the parameters have been calculated as 1/2 gamma(10, 2.5), and | 2 normal(4.1, 2/20).

a) Sample at least 5,000 y values from the posterior predictive distribution.

b) Form a 75% quantile-based confidence interval for a new value of Y .