Warning:this is written image from my mind RAM
i- What is the probability of success in probability exam, given you are study hard?
ii- What is the probability of success in the 2 probability Exams given first is final and second is Midterm !, repeat for the swapped?
iii- Let the probability of return to home after probability exam modeled as stochastic process also can shown as cont. Markov chain
Assume the system is consists of the country nodes "Egypt cities" the probability transition matrix can formed by the ways"i.e. roads/highway ", what is the probability to forced to go to Mansoura "as Destination " from "Cairo" using this Path, Cairo, New Cairo's cities, Cairo-Ismaellia desert way, Ismallia, Port Saead, Manzalla, Decernes, and then finally Mansoura. Assume No hidden Markov chain.
v- Using Markov Chain, Deduce an algorithm to solving "drunk sales man problem" Hint starting from the sales man problem,
and then:-
a- find limiting probability if the visiting to each city not exceed 2 times.
b- find Mean recurrence time for each state.
c- find the periodic states if exist.
d- assuming the count problem belong to Poisson distribution, Find N(t) for each state.
iv- Transform the binomial vector distribution X to Y which is 4th Order Deferential Equation, assume any missing data. Also comment about Jacobin for higher derivative.
Asking for the aim of exams.. the goal of exams.. I would like to know .. not just for passing exams .. not just act as buffer .it is enough.. I will searching for the know how forever... but I am Dissatisfied.. simply it may act as breakaway.
