A weapon system (WS) has a limited “memory”; it can acquire and store in its memory up to K targets. The targets are acquired sequentially until the memory is full. Upon the acquisition of the K-th target, all targets in the WS memory are instantaneously engaged and killed with certainty. Then the process repeats. Time is discrete and at each time period at most one target can be acquired. The probability of acquiring a target in a certain time period is p. Let Xn denote the number of targets that have been acquired at the end of time period n. (a) Why is { Xn} a Markov chain? What is its state space? (b) Let K=3. Give a transition matrix for { Xn}.
Added by Rohan R.
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The state space of the Markov chain is the set of all possible values that Xn can take, which in this case is {0, 1, 2, 3, ...}. ** Show more…
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