No abstract

Context plays a significant role in teaching probability and statistics; although its importance has been contended in previous studies, there is not sufficient research on the role of context. Therefore, this study aimed to clarify the actual use of context in problem solving through pre-service mathematics teachers. We focussed on the Tuesday Birthday Problem, which requires awareness of context. Data were obtained from surveys involving 98 teachers and analysed by classifying answers based on the answer types related to context. Results revealed that there are three hurdles related to context in this problem: ‘generation of the idea of conditional probability,’ ‘identification of the necessary and sufficient context for the condition,’ and ‘correct use of the context.’

-In this paper, a Pareto optimal strategy for uncertain Markovian linear stochastic system with multiple decision makers is investigated. By applying the guaranteed cost control principle, a set of conditions, wherein the stochastic system is exponentially mean-square stable (EMSS) and has a cost bound, is obtained using the stochastic algebraic Riccati inequality (SARI). In addition, the minimization problem of the cost bound is formulated. It is shown that the necessary conditions can be derived by a set of crosscoupled stochastic Riccati equations (CCSAREs).