utes, and she receives messages from her brother every 30 minutes. (a) Find the probability that by 7:30 a.m. Mary receives exactly four messages - two of her best friend and two of her mother. (b) With a chance of 75% a text message contains a typo independent of the sender. Find the probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m. 5. (10 points) Consider a continous-time Markov chain (Xt)tzo with state space S = {1, 2, 3, 4). From state 1 the process is equally likely to either transition to 2 or 4; from state 2 and 3 the process is equally likely to transition to all other states; and from state 4 the process always transitions to state 1. Suppose further that the process spends on average vi units of time in each state i e S. a Provide the transition probability matrix P for the embedded chain. (b) Provide the holding time parameters. c Provide the generator matrix Q. Justify your answer. (d) Draw the transition rate graph. Page 2 of 2 acer