Statistics of Measurement¶
Overview¶
In the first question, you will simulate random die throws, including the distribution of multiple N-sided dice. You will also visualise the two-dimensional probability distribution for the sum of two dice. Additionally, you will investigate the sum of an arbitrary number of N-sided dice both numerically and analytically.
Next, you will investigate two scenarios of the Monty Hall problem numerically. You will explicitly simulate multiple iterations of the game show scenarios in order to test your previous hypotheses regarding door switching.
Thirdly, hypothesis testing, chi-square tests, and type I errors will be investigated. You will carry out hypothesis tests for continuous distributions and parameter estimation using both maximum likelihood estimation and minimisation of the chi-square statistic.
The final question will combine the central limit theorem (CLT) and hypothesis testing, using the functions you created in the first question.
Notes¶
Ensure that all tasks are repeatable by seeding the random number generator you choose to use. You may have to do this for every cell in your notebooks in order to ensure that the output of each cell is repeatable, independent of the order in which (or number of times) they are run.