To illustrate the use a Markov chain model to investigate relationship between a

Question

To illustrate the use a Markov chain model to investigate relationship between a weapon's probability of kill and the survival of the shooting platform and the number of targets killed An air defense targeting radar can emit continuosly or intermittently while engaging an aircraft. If it emits continuously, it will detect and kill the aircraft with probability 0.9 If it emits intermittently, it will detect and kill the aircraft with probability 0.6 Continuously emitting radar will be killed while it is engaging an aircraft with probability 0.8 by a standoff platform. Intermittently emitting radar will be killed while it is engaging an aircraft with probability 0.3 by a standoff plaltform. Suppose the radar will engage two aircraft sequentially, one at a time. Assume that radars either always emit continuously or always emit intermittently. Also assume survival of the players is independent for the 2 engagements. Assume that during an engagement the aircraft is killed or not killed before the radar is killed or not killed. Compute the probability the radar is still alive after targeting 2 aircraft. Compute the expected number of aircraft killed. Compare the virtues of radar emitting continuously or emitting intermittently.

Explanation / Answer

here let us assume the radar is emitting continuously.

if the radar gets engagement with two air crafts then it will kill the the one air craft while engaging due to continuous emission and the probability will be 0.9

and also the radar will be killed while it is engaging with the air craft with the probability 0.3

therefor the radar will be survived that is not killed while the air crafts will be killed.

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