Poisson Distribution
This is an introduction to Poisson Processes and the Poisson Distribution. [Probability playlist: Lesson 27 of 29]
This lesson explains more of the drivation of the Poisson Distribution. [Probability playlist: Lesson 28 of 29]
The EJS Radioactive Decay Model simulates the decay of a radioactive sample using discrete random events. It displays the number of radioactive nuclei as a function of time. You can change the initial number of nuclei and the decay constant as well as changing the plot to a semi-log plot.
A suite of VBA simulation programmes used at first year level containing a number of tools for teaching introductory statistics at university level. Note that these are written for MS Excel 2007 (or later versions). The modules roughly follow chapters in the first year statistics textbook, Introstat (LG Underhill) and essentially support and supplement that book. They are to a significant extent self explanatory for those with some knowledge of statistics and simulation.These modules are essentially crafted as teaching tools and the experience of first year students would be of the lecturer leading the students through the simulations at an appropriate pace, allowing plenty of opportunity for discussion and clarification. Lab based tutorials also support this process.Module 1: We discuss the question: What are random numbers and what is a statistical distribution? We introduce the Uniform distribution, the most simple of statistical distributions. Module 2: In order to test a claim that a set of 5 mice have been taught how to navigate a maze, we explore the chances of different numbers of successful mice, under the assumption that the mice are making purely random choices. This supports a discussion of how the Binomial distribution arises. Module 3: We sketch the following scenario: a stretch of road is surveyed to determine the number of potholes. Unfortunately information on the individual positions of the potholes is lost but the total number of potholes is correctly recorded. We manage to salvage the situation from embarrassment by employing the Poisson distribution to good effect! Module 4: The same situation pertains as in module 3; however we focus our efforts on the chances of finding stretches of road without potholes, and discover the exponential distribution. Module 5: We explore the magical effects of averaging and find a surprising commonality across the distributions of averages arising from a multitude of different situations (give or take a few assumptions they all seem to converge to that bell shaped curve?). Module 6: We consider hypothesis testing and attempt to pin down the chances that weŐre wrong when we think weŐre rightÉor is it right when we think weŐre wrong? Oh yes, we also look at statistical powerÉdo we have enough information to attempt to adjudicate between these two hypotheses anyway? Module 7: We find a relationship between two variables and express this as a mathematical straight line formula. But the actual line we get depends on the sample we have. We explore how certain we can be that we know anything about the relationship between our two variables at all.
This module introduces Poisson Distribution and gives an example of its application. It also includes an exercise to engage the reader.
This module introduces queuing theory, its applications in telephony, and solutions to queuing problems. There is also an exercise to engage the reader.
