Roll a fair die repeatedly and let Y 1 ;Y 2 ;::: be the resulting numbers. Let X n D jfY 1 ;Y 2 ;:::;Y n gj be the number of values we have seen in the first n rolls for n ? 1 and set X 0 D 0. X n is a Markov chain. (a) Find its transition probability. (b) Let T D minfn W X n D 6g be the number of trials we need to see all 6 numbers at least once. Find ET.

(co 3) the soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. the company takes readings of every 10th bar off the production line. the reading points are 5.8, 5.9, 4.9, 6.5, 5.0, 4.9, 6.2, 5.1, 5.7, 6.1. is the process in control or out of control and why? it is out of control as two of these data points are more than 2 standard deviations from the mean it is in control as the data points more than 2 standard deviations from the mean are far apart it is out of control as one of these data points is more than 3 standard deviations from the mean it is in control as the values jump above and below the mean