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Basic knowledge of probability theory and statistical methods.
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One comes across Statistics in daily life everywhere. What is meant with a “statistically significant result”? How should one interpret a confidence interval? What can we do with an estimated annual return on investment of 4%? Results in the past are not a guarantee for future results: yes, but what value do statistical predictions have?
In statistics probability theory is applied. Therefore we will discuss the basic concepts of probability and their applications first. After that Bayes’ rule will not have any secrets for you anymore and at the end we will see that the expected value of conditional expectation is the same as the unconditional expectation. Probability theory supplies many different models (distributions) for various practical situations. Probably the binomial distribution (discrete) and the normal distribution (continuous) are known to you from prior education, but we will add more models, such as the hypergeometric distribution and the exponential distribution.
Basic statistics consists of 4 parts: descriptive statistics, estimation, confidence intervals and testing of hypotheses. We will compare possible estimators and discuss the estimation errors. These errors are incorporated in estimation intervals, the so called confidence intervals. Is a diet effective for losing weight? In order to answer this kind of questions, the concepts of testing hypotheses are introduced and applied in in one and two samples problems for binomial or normal situations. In an eight steps procedure a systematic approach is learned. Being able to compute intervals and to decide whether to reject a hypothesis is important, but giving a correct interpretation of results is even more important.
Probability and Statistics are topics which you have to practice: solving exercises, often in a business context, is necessary to really understand how the theory can work in practice.
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