The flow interruption data for the $10$ systems are contained in the WinBUGS file feedwater data.ode. Check the model, load the data, compile the model, and generate initial values for three chains. Specify that the nodes alpha, beta and lambda should be monitored, and generate three chains of simulated values, each of $2000$ iterations.Do you think that WinBUGS used a special MCMC adapting algorithm to do the sampling? Justify your answer.$($d$)$ With reference to suitable trace plots, discuss what number of iterations seems suitable for the burn$-$in phase. It is necessary to include trace plots only for alpha and beta in your answer, though your discussion should also mention those for lambda.$($e$)$Whatever you concluded in part $($d$),$ use a burn$-$in of $500$ iterations for this part. Report estimates of the posterior means, standard deviations and equal$-$tailed $95\%$ credible intervals for $11$ and $12.$ Is there evidence that generating system $2$ is more prone to feedwater interruptions than generating system $1,$ or could the difference between them be attributed to random variation?