Conclusion
Following completion of this free OpenLearn course, Univariate continuous distribution theory, you should find that your understanding of the mathematical theory underlying the methods and concepts used in practical statistical analyses is improving.
You should now be able to:
- understand the properties of probability density functions and cumulative distribution functions
- define expectation, and be introduced to its important linearity property
- calculate raw moments and central moments, including their special cases, the mean and variance
- understand the effect of linear transformation on mean, variance and density
- calculate the moment generating function, and appreciate its link to moments.
This free OpenLearn course is an extract from the Open University course M347 Mathematical statistics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .
If you feel you are ready to move on in your study of statistics but don’t have time to study a full Open University course at this time, you might like to study the free OpenLearn courses Point estimation, another adapted extract from the Open University course M347 Mathematical statistics, or Modelling events in time, an adapted extract from the Open University course M343 Applications of probability.
If you are interested in pure mathematics, you might like to try the free OpenLearn courses Number theory, Group theory, Rings and polynomials and Metric spaces and continuity.
If you are interested in applied mathematics, you might like to try the free OpenLearn courses Linear programming – the basic ideas, Introduction to the calculus of variations and Kinematics of fluids.