4.7 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|0,02) = .31dnorm(y, 0,0) + .46dnorm(201, 20)+.23dnorm(y, 301, 30) where the posterior distributions of the parameters have been calculated as 1/02 ~ gamma(10,2.5), and 002 ~ normal(4.1, 02/20). a) Sample at least 5,000 y values from the posterior predictive distribu- tion b) Form a 75% quantile-based confidence interval for a new value of Y. 4.7 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|0,02) = .31dnorm(y, 0,0) + .46dnorm(201, 20)+.23dnorm(y, 301, 30) where the posterior distributions of the parameters have been calculated as 1/02 ~ gamma(10,2.5), and 002 ~ normal(4.1, 02/20). a) Sample at least 5,000 y values from the posterior predictive distribu- tion b) Form a 75% quantile-based confidence interval for a new value of Y