The fundamental matrix of the general random walk with absorbing chain - application to student flow in an educational institution

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June, 2016
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This paper presents an application of Markov Analysis of student flow in an educational institution. Historical data of random sample of 1200 students of Kwabenya Atomic Cluster of Schools was investigated. Was first shown that, the Fundamental Matrix of the Markov Analysis can be determined in elementary manner via the adjugate of matrix (I – Q). The Fundamental Matrix of Markov Chain is the inverse of the matrix (I – Q) where Q results after matrix P have been partitioned into canonical form. P is a transition probabilities matrix with entries Pij which satisfy conditions (i) Pij ≥ 0 (ii) ∑Pij = 1. i Results indicated that: (i) a first year student has about 0.93 probability of graduating (ii) first year, second year students stay on average of four (4) terms at their respective levels before they pass on to the next level of study, while senior students stays an average of two (2) terms (iii) A third year student has a probability of one (1) of progressing to graduation stage. Thus, there is a certainty that a student would progress to graduating stage once he/she get to the senior stage. (iv) A percentage of 6.6% of incoming first year students withdraw from their study and (v) the probability of progression to a higher level and graduating increases as students move on to a higher level in the system
A thesis submitted to The Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the degree of M.SC Industrial Mathematics,