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    Keywords
    Article
    Application of Three Probability Distributions to Justify Central Limit Theorem
    Okoro Ifeanyichukwu, Uka Christian O., Ogbara Chidi Obed
    October 22, 2023•DOI: 10.52589/AJMSS-LHCUQZLF•Volume 6 Issue 4•2,250 views
    This paper focused on the use of three probability distributions to justify the central limit theorem (CLT). The aim was to use the moment generating function (MGF) to prove (CLT) and also to portray the shape of different sample sizes (15, 30 and 100) of distributions of sample means on a histogram. The population distributions studied were: Normal, Gamma and Exponential distributions. In addition, sampling distribution of the mean table was constructed for better understanding of CLT. The study used simulation to simulate population distribution of Normal, Gamma and Exponential. Five hundred (500) distributions of sample means were drawn from each of the simulated population distributions at three different sample sizes (n): 15, 30 and 100. The shape of the simulated population distribution and sampling distribution of mean were presented on a histogram. The mean and standard deviation of each population distribution together with distribution of sample means at different sample sizes were also presented on the histogram plotted. The findings showed that under normal distribution, the sampling distribution of mean produced a shape like normal distribution irrespective of the sample size. Conversely, the shape of sampling distribution of mean under non-normal distributions gradually converges to normal distribution as sample size tends to infinity, while the variability of each sampling distribution decreases as the sample size increases. Therefore, CLT holds for large sample size (n ≥ 30). Read more
    Keywords:Central limit theoremsampling distribution of meannormal distributionexponential distributionGamma distributionhistogram.
    Journal
    Journal of Dental and Oral Health Research

    Journal of Dental and Oral Health Research (JDOHR) is an international peer-reviewed open access journal that publishes original research in dentistry, oral health, craniofacial sciences, and related healthcare disciplines. The journal provides a platform for the dissemination of high-quality basic, clinical, translational, and applied research that advances understanding of oral diseases, dental practice, oral healthcare delivery, and preventive dentistry. JDOHR welcomes contributions that improve oral health outcomes, enhance clinical practice, and promote innovation in dental science, education, and patient care.

    Journal
    Journal of Clinical Psychology and Counselling

    Journal of Clinical Psychology and Counselling (JCPC) is an international peer-reviewed open access journal that publishes original research in clinical psychology, counselling, mental health, psychotherapy, and related behavioural sciences. The journal provides a platform for the dissemination of high-quality theoretical, empirical, and applied research that advances understanding of psychological wellbeing, mental health disorders, human behaviour, and therapeutic interventions. JCPC welcomes contributions that enhance evidence-based psychological practice, counselling services, mental health education, and the promotion of individual, family, and community wellbeing across diverse cultural and clinical contexts.

    Journal
    Journal of Infectious Diseases and Clinical Epidemiology

    Journal of Infectious Diseases and Clinical Epidemiology (JIDCE) is an international peer-reviewed open access journal that publishes original research in infectious diseases, clinical epidemiology, public health, microbiology, and related biomedical disciplines. The journal provides a platform for the dissemination of high-quality basic, clinical, translational, and population-based research that advances understanding of infectious diseases and their impact on individuals, communities, and health systems. JIDCE welcomes contributions that enhance disease prevention, outbreak investigation, surveillance, diagnosis, treatment, and control through rigorous scientific inquiry and evidence-based approaches.

    Journal
    Journal of Security and Criminology

    Journal of Security and Criminology (JSC) is an international peer-reviewed open access journal that publishes original research in criminology, security studies, criminal justice, policing, forensic science, and related social science disciplines. The journal provides a platform for the dissemination of high-quality theoretical, empirical, and policy-oriented research that advances understanding of crime, security threats, justice systems, social order, and public safety. JSC welcomes contributions that explore the causes, consequences, prevention, and control of crime, as well as emerging security challenges affecting communities, institutions, and nations in an increasingly interconnected world.