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 SCI 212 - Theory of Statistics and Data Analysis

Content

The course SCI 212 Theory of Statistics and Data Analysis provides a mathematical and theoretical foundation for statistics and various statistical techniques as they are used in the courses ACC 110 and ACC 210 - Methods and Statistics I and II, respectively. The course starts by introducing the sample space as the set of all possible outcomes of experiments. Events split this sample space into two parts; since an event occurs or does not occur. Set theory allows for defining the (exclusive) union, intersection and difference of various events. This forms the foundation of probability. Random variables are introduced to assign a real number to each possible outcome of an experiment; to each element in the sample space. These random variables have probability distributions with a certain mean and variance and are characterized by moment generating functions. Combinations of random variables amount to joint probability density functions; independent random variables, covariance and correlations between random variables will be discussed. Numerous discrete and continuous parametric distributions will be discussed in detail; for instance, Bernoulli, Binomial, Poisson, Uniform, Gaussian, Exponential, Gamma and Chi-Squared distribution. It is shown explicitly that under certain conditions distributions can be approximated by the Normal Distribution. This leads to the Central Limit Theorem. 


The course then continues with discussing sample statistics: what is the distribution of the sample mean if the underlying random variable has, for instance, a Bernoulli distribution. Sample statistics for the Normal distribution will be discussed in detail. The next step is to use a random sample to estimate the parameters of the underlying probability distribution. The method of moments will be discussed and maximum likelihood estimators will be introduced. A very important class of maximum likelihood estimators are the least squares estimators. The method of least squares will be presented in detail. Finally, the course will discuss Student's t-test and Fisher's F-distribution. If there is time left, the technique of Principal Component Analysis (PCA) will be discussed.

 

Instructor

 

Track

Mathematics

 

Prerequisites

The following course is required in order to take this course:

  • SCI 111 Mathematical Ideas and Methods in Contexts

Required for

This course is required in order to take the following course:

  • SCI 311  Signals and Systems
  • SCI 312  Advanced Mathematics
  • SSC 366 Econometrics