4. Suppose that the following data were obtained from the records of a certain two yearcollege: Of those who were freshman (F) during a particular year, 80% become sopho-mores (S) during the next year and 20% dropped out. Of those who were sophomoresduring a particular year 90% graduated (G) by the next year and 10% dropped out.(a) Create a transition diagram that describes this scenario.(b) Create a transition matrix that describes this scenario. Is this scenario ergodic orabsorbing? Explain.(c) Suppose that this year, there are an equal percentage of freshmen and sophomores.Use matrix multiplication to determine what percentage will have graduated in 5years? What percentage will have dropped out?(d) Rewrite the matrix in standard form.(e) Find N, R and B.(f) Determine the probability that a student who begins as a freshman will drop out.(g) Determine the probability that a student who has made it to sophomore year willdrop out.(h) Determine the probability that a student who begins as a freshman will graduate.(i) Determine the probability that a student who has made it to sophomore year willgraduate.

"Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get the remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.” Given that, of those who were freshmen (F) during a particular year, 80% become sophomores(S) during the next year and 20% dropped out. Of those who were sophomores during a particular year 90% graduated (G) by the next year and 10% dropped out.(a) The transition diagram that describes the given scenario :(b)The transition matrix that describes the given scenario : Let the state drop out is denoted by D The states F0 and F1 denotes year 1 starting and year 1 ending. F0F1SDGP=F0F1SDG10000000.80.200000.10.90001000001 The absorbing boundary condition is PXn+1=0/Xn=0=1 PXn+1=0/Xn=0=1 PXn+1=5/Xn=5=1 It is an absorbing Markov chain since it satisfies the absorbing boundary condition. (c) Given, there are an equal percentage of freshmen and sophomores. X5=X0P5 P2=10000000.80.200000.10.90001000001×10000000.80.200000.10.90001000001=100000000.280.720000.10.90001000001 P4=P2×P2=100000000.280.720000.10.90001000001×100000000.280.720000.10.90001000001=100000000.280.720000.10.90001000001 P5=P×P4=10000000.80.200000.10.90001000001×100000000.280.720000.10.90001000001=100000000.280.720000.10.90001000001 X0=00.50.500 X0P5=00.50.500100000000.280.720000.10.90001000001=0000.190.81 The percentage will have graduated in 5 years is 81% The percentage will have dropped out in 5 years is 19%