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This programme introduces the course by examining the way probability models can be used in experimental and everyday situations.
Module code and title: M341, Fundamentals of statistical inference M341; 01 17-03-1977 1977 00:25:00 + Show more... Robert Clamp Stanley Collings; A. Daniel Lunn; Adrian Smith BBC Open University Accidents; Geiger-Rutherford apparatus; Haemocytometer; Poisson Shots of an instrument which monitors number of alpha particle emissions, from a radioactive source, in fixed intervals of time. Stanley Collings introduces the programme. Daniel Lunn with a reconstruction of the 1910 Geiger - Rutherford apparatus which investigated emission of alpha particles from a radioactive source. He explains how the apparatus works and then conducts the experiment. A histogram of alpha particle emissions is produced. Adrian Smith explains why a model is needed to make the data meaningful. Using animated diagrams, he makes some assumptions which would build up a probability model to account for the alpha-particle emissions. The model's mathematical expressions are captioned as he talks. Smith demonstrates that the emission distribution in this experiment follows a Poisson distribution. Smith, using a graph plotter, explains how one determines which member of the family of Poisson distributions to choose to represent the predicted distribution for the model. He places the observed distribution over the predicted distribution and comments on the fit. Daniel Lunn reviews the assumptions used in the model above and then suggests that these could be when modelling other situations. Still shot of a man being kicked by a horse. Lunn then goes on to apply these assumptions and the Poisson distribution to a haemocytometer in order to model and predict the distribution of yeast cells. The data for this experiment is displayed on a VDU and a histogram is plotted by graph plotter. The observed and predicted distributions are compared. Smith briefly reviews the alpha-particle experiment and goes on to propose a variant of this experiment. Here a prediction is made before the actual distribution is seen. Smith seeks to predict the time intervals between emissions: The mathematics are captioned as he talks. He arrives at the negative exponential function which he suggests is a model for the actual distribution. The graph plots a negative exponential function. Daniel Lunn runs the experiment and compares the results with Smith's prediction above. Smith points out that the assumptions used above can be applied to other experiments. Shots of a road T-junction showing cars arriving at different times. Shots of a VDU which displays the data collected from the T-junction. Shot of histogram showing the distribution of arrival times of cars. The graph plotter then plots a negative exponential function over this histogram and the two are compared by Smith. Lunn reviews the procedures which were set up in the above experiments. These are captioned in a flow diagram. Smith tries to make a Poisson distribution work for predicting the distribution of factory accidents. Real data of factory accidents is plotted and the Poisson distribution is then plotted on top of this. Smith comments on the fit. He goes on to plot a mystery distribution (not a Poisson) over the two distributions above. This one fits the data much better. 6HT/72248 00525_4230 1112 no