ETD Collection

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Subject: search.filters.subject.Probabilities

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    Annual peak rainfall data augmentation - A Bayesian joint probability approach for catchments in Lesotho
    (2017) Kanetsi, Khahiso
    The main problem to be investigated is how short duration data records can be augmented using existing data from nearby catchments with data with long periods of record. The purpose of the investigation is to establish a method of improving hydrological data using data from a gauged catchment to improve data from an ungauged catchment. The investigation is undertaken using rainfall data for catchments in Lesotho. Marginal distributions describing the annual maximum rainfall for the catchments, and a joint distribution of pairs of catchments were established. The parameters of these distributions were estimated using the Bayesian – Markov Chain Monte Carlo approach, and using both the single-site (univariate) estimation and the two-site (bivariate) estimations. The results of the analyses show that for catchments with data with short periods of record, the precision of the estimated location and scale parameters improved when the estimates were carried out using the two-site (bivariate) method. Rainfall events predicted using bivariate analyses parameters were generally higher than the univariate analyses parameters. From the results, it can be concluded that the two-site approach can be used to improve the precision of the rainfall predictions for catchments with data with short periods of record. This method can be used in practice by hydrologists and design engineers to enhance available data for use in designs and assessments.
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    Extensions of the first Borel-Cantelli Lemma in Riesz spaces
    (2018) Mushambi, Nyasha Takunda
    The classical First and Second Borel-Cantelli theorems as well as the Kolmogorov Zero-One Laws have been extended to the abstract setting of Riesz spaces by Wen-Chi Kuo, Coenraad C. A. Labuschagne and Bruce A. Watson. This dissertation aims to extend upon the work of these authors. In particular, an extension of the Barndorff-Nielsen Zero-One Law to the Riesz space setting.
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    Creating opportunities to learn through resourcing learner errors on simplifying algebraic expressions in Grade 8
    (2017) Matuku, Olinah
    This research problematised the teaching and learning of the grade 8 topic of simplifying algebraic expressions via the errors and misconceptions learners’ show on that topic. The study conducted at a secondary school in Johannesburg identified the nature of grade 8 learners’ errors and misconceptions on simplifying algebraic expressions. A teaching intervention through using those errors as resource to help learners reduce them was undertaken. There was an implementation of discovery learning as an intervention strategy to help learners to explore algebraic concepts with the minimum involvement of the researcher. The researcher used constructivism, sociocultural learning and variation theories since these theories affect the learners learning of algebra. The researcher used an interpretive paradigm which is concerned about the individuals’ interpretation of the world around them. Purposive and convenience sampling were used in the study. Data was collected using a sample of thirty grade 8 learners. The learners wrote a pre-test as one of the assessment task in the study. The purpose of the pretest was to identify learners’ errors on simplifying algebraic expressions. After the learners’ errors were identified and analysed, the researcher conducted a semi-structured, focus group interview with six learners in the study. The selection of the interviewees depended on the type and frequency of errors they have displayed in their pre-test scripts. The purpose of the interview was to investigate the reasons behind the learners’ errors as identified in the pre-test. An intervention strategy which implemented guided discovery learning was employed to learners with the use of the identified errors as a resource to help learners reduce them. After the intervention, the learners wrote a post-test to check if there was an improvement in learners’ performance after the intervention. Pre- and post-tests results were analysed for errors revealed by learners. The teaching intervention periods were introduced to create learning opportunities for learners. The findings of the study revealed that before intervention learners encountered a lot of difficulties when simplifying algebraic expressions but the learners’ performance improved after the intervention. The recommendations of the study are, teachers should welcome learners’ errors in teaching and learning of mathematics and use them as a resource to help learners reduce them in solving mathematical problems Key words: Learners’ errors, misconceptions, simplification of algebraic expressions.