Basic Mathematical Statistics
Basic Mathematical Statistics Mathematical statistics deals basically with situations which can be described as follows: Given a population of statistically identical, independent elements with unknown (statistical) properties, measurements regarding these properties are made on a (random) sample of this population and, on the basis of the collected data, conclusions are made for the remaining elements of the population. Examples are the parameter estimation for the distribution function of an item's failure-free operating time 't, or the decision whether the expected value (mean) of't is greater than a given value. Mathematical statistics thus goes from observations (realizations) of a given (random) event in a series of independent trials and searches for a suitable probabilistic model for the event considered (inductive approach). Methods used are based on probability theory and results obtained can only be formulated in a probabilistic language. Minimizatio...