by Jimbo Henri Claver, Jawad Azimi and Takeru Suzuki
Original Research
We present a mathematical formulation of the Multiple Dice Rolling (MDR) game and develop an adaptive computational algorithm to simulate such game over time. We use an extended version of the well-known Chapman-Kolmogorov Equations (CKEs) to model the state transition of the probability mass function of each side of the dice during the game and represent the time-dependent propensity of the game by a simple regression process, which enable to capture the change in the expectation over time. Furthermore, we perform a quantitative analysis on the outcome of the game in a framework of Average Probability Value (APV) of appearance of a side of the dice over trials. The power of our approach is demonstrated. Our results also suggest that in the MDR game, the APV of appearance of a side of a dice can be appropriately predicted independently of the number of sides and trials.
American Journal of Applied Mathematics and Statistics. 2017, 5(5), 169-174. DOI: 10.12691/ajams-5-5-3
Pub. Date: December 26, 2017
10341 Views2721 Downloads1 Likes
by Okeke Evelyn Nkiruka, Okeke Joseph Uchenna, Yawe Ayuba, Anule Josaphat and Bello Abdulrasheed
Original Research
Over the years, efforts have been made by researchers in studying the effects of certain factors on academic performance of students, though with little concentration on the primary section of education. This research therefore worked on the academic performance of pupils in primary school. Variation in the analyzed performance and the factor(s) causing the variations were studied using factor analysis. The data used is a secondary data, collected from Federal University Wukari Staff School and it’s on the terminal examination scores of the pupils in seven selected subjects over one selected academic session (2015/2016). From both the un-rotated and rotated factor analysis results, we observed a fair relationship between the mathematical and less mathematical subjects, though they present the major variation in the pupils’ performance to be in the less mathematical subjects like English Language, Verbal Aptitude, Social Studies, Creative Art, and Religious Studies. Also, the analysis presented three factors (gender, age, and environment) to be the cause of the variation between the pupils performance in primary school.
American Journal of Applied Mathematics and Statistics. 2017, 5(5), 164-168. DOI: 10.12691/ajams-5-5-2
Pub. Date: December 07, 2017
7855 Views1794 Downloads
by E. N. Bereslavskii
Original Research
Within the framework of the theory of plane steady filtration of an incompressible fluid according to Darcy’s law, two limiting schemes modeling the filtration flows under the Joukowski tongue through a soil massive spread over an impermeable foundation or strongly permeable confined water bearing horizon are considered.
American Journal of Applied Mathematics and Statistics. 2017, 5(5), 159-163. DOI: 10.12691/ajams-5-5-1
Pub. Date: November 29, 2017
9526 Views1792 Downloads