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Writer's pictureClement Twumasi

Central Limit Theorem Proof, Bootstrapping & Jackknife Estimation Techniques/Schemes (5th Lesson)

Prior knowledge of programming and statistics are not required. It's only a good introduction and we will continue every Saturdays with more advanced tasks. The main goal is to develop the interest of mathematical programming among students from Africa. However, anyone who interested is welcome to join and learn. This class will be a good introduction to data analysis with advanced statistical software like R.


For general information about the class, please visit the link below: https://piazza.com/clements_school_on_data_analysis/fall2020/ss401/info?fbclid=IwAR2UkhqecbiBx3RQdetmRt4wPsNmyEe3y7RtK9PrfO68DaNaZLY5P3Ilnuw


For the personal profile of the instructor/tutor, click below:

https://f36d003f-d71d-49cc-9fea-cbb325732ca8.filesusr.com/ugd/779116_8b81a5793af94ccdadec45b62b49cfcd.pdf


Personal website: https://twumasiclement.wixsite.com/website Below summarizes the content of this YouTube video (from Saturday's class dated Nov 14, 2020):


1. Solving a few selected questions in the last week's assignment tasks Extract all multiples of 12 from 10 to 100000 (save results as a vector & list respectively) using i) for loop and ii) while loop


2. Create a Monte Carlo Simulation to describe the outcome of pregnancy for 100 women at birth (number of runs=100) who can either give birth to a male or female. Note that male and female babies are equally likely to be born (probability of 0.5 respectively). Record the total number of woman who gave birth to males and female respectively out of the 100 women from the Monte Carlo Simulation. Using a barplot, plot the proportion of male and female borns. Increase the number of women to 1000, and compare the findings with that of the 100 women.


3.Simulating samples from probability distributions (exponential, normal, lognormal, Poisson, uniform and binomial distributions).


4. Prove the Central Limit theorem of at least the mean based on simulated samples from different probability distributions.


5. Use Bootstrapping & Jackknife estimation techniques to estimate and bound unknown parameters such as population means, population proportions, etc.



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