The legal system in Nigeria is be-deviled with delayed justice which has become a source of concern to many person. This is very much peculiar to those who feel that the judiciary is too slow in resolving legal issues in Nigeria. In Nigeria, there abound court cases especially those of criminal dimensions that have ongoing for years now without reaching a conclusive conclusion. The study is aimed at modelling the queuing system in the magistrate courts in Onitsha Magisterial districts. The specific objectives include: to apply the M/M/2 and M/M/3 models with identical and parallel queues to criminal cases in the Magistrate court and to compare the efficiency of the two models and in either cases to determine time to justice in criminal cases in the Magisterial District. The results of the study show that M/M/2 model with 2 identical and parallel queues have an expected number of cases in the system as 39 with 50% idle time while the M/M/3 model with 3 identical and parallel queues have an expected number of cases in the system as 23 cases with 64.88% idle time. The comparison of the two models shows M/M/2 with 2-identical and parallel queues is more efficient as it has more number of cases to attend to and less idle time. The study therefore concludes that the delays in the disposal of cases especially those with criminal nature may not be attributable to the queuing systems in place. Even though lesser number of servers is seen to be efficient, this may not be advised. Increasing the number of servers though will increase speed of disposal of cases, may also lead to increased idle time of servers. As more courts being set up may result in waste of resources, manpower and time as the 2-server system is efficient in speeding up justice delivery in the magisterial division.

In Multiple regression analysis, it is assumed that the independent variables are uncorrelated with one another, when such happen, the problem of multicollinearity occurs. Multicollinearity can create inaccurate estimates of the regression coefficients, inflate the standard errors of the regression coefficients, deflate the partial t-tests for the regression coefficients, give false p-values and degrade the predictability of the model. There are several methods to get rid of this problem and one of the most famous one is the ridge regression. The purpose of this research is to study the performance of some popular ridge regression estimators based on the effects of sample sizes and correlation levels on their Average Mean Square Error (AMSE) for Poisson Regression models in the presence of multicollinearity. As performance criteria, average MSE of k was used. A Monte Carlo simulation study was conducted to compare performance of Fifty (50) k estimators under four experimental conditions namely: correlation, Number of explanatory variables, sample size and intercept. From the results of the analysis as summarized in the Tables, the MSE of the estimators performed better in a lower explanatory variables and an increased intercept value. It was also observed that some estimators performed better on the average at all correlation levels, sample sizes, intercept values and explanatory variables than others.

Making an appropriate decision in the selection of sustainable club from other clubs studied involves the use of right statistical approach, hence the need for stochastic and game theory analysis of English premier league scoreline. The following clubs Manchester United (MU), Chelsea (C), Arsenal (A), Manchester City (MC), Liverpool (LP), Tottenham (T) and Everton (E) were studied for both home and away matches for the period of 2010/2011 to 2019/2020 season. The optimal strategy and overall optimal strategy for MR G and MR B were obtained for each season and the 10 seasons respectively. The result showed that Manchester United has the highest probability (0.29) of being selected by MR B and Liverpool has the probability of 0.27 of being selected by MR G. The matrix of flow was also obtained when Manchester United played against Liverpool, given that Manchester United is home, as WWWLWWDWDD, and when Manchester United is away and Liverpool home, as WDLWLLDDWW. The two and four step transition matrix was also used to predict the future matches and their probabilities obtained given the probabilities of the previous game. The limiting distribution of the transition probability matrix obtained showed that Manchester United has a 67% chance of winning Liverpool while Liverpool has a 33% chance of winning Manchester United, this shows that Manchester United is stronger at home. Thus, the two most sustainable clubs out of the seven clubs studied are Manchester United and Liverpool.

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