3. Batman has gone out for a night of crime ghting to an alley frequented by criminals. Criminals arrive to the alley according to a Poisson Process with rate of 1 per 5 minutes. Using standard had guys techniques, they only attack the Dark Knight one at a. time. It takes our hero an exponential amount of time to knock each one out with an average of 1 minute. Due to the size of the alley, there can he at most 5 conscious criminals. Develop a CTMC model for number of conscious had guys. [a Give the Q matrix, draw the TPD, and solve for or. J {h} What is the expected number of conscious criminals in the alley? {c} {d} Is this a hirthanddeath process? \"Why or why not? If it is, recalculate the steadystate vector utizing the special equations derived for a BAD process. Show all relevant formulas for full credit. If Batman is in the alley for 2 hours, how long does he spend actually ghting