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Going through an IFoA past paper question regarding the central limit theorem and how to apply it to the exponential distribution to find approximate probabilities Find all IFoA past papers & memos at the following link: www.actuaries.org.uk/studying/prepare-your-exams/past-exam-papers-and-examiners-reports

Going through an IFoA past paper question regarding the central limit theorem, moment-generating functions, and the relationships between Gamma, Exponential and Chi-Squared distributions Find all IFoA past papers & memos at the following link: www.actuaries.org.uk/studying/prepare-your-exams/past-exam-papers-and-examiners-reports

Going through an IFoA past paper question regarding the central limit theorem and it's applications to the sampling distribution of the mean as well the t-distribution Find all IFoA past papers & memos at the following link: www.actuaries.org.uk/studying/prepare-your-exams/past-exam-papers-and-examiners-reports

Going through an IFoA past paper question regarding the central limit theorem and it's application to a random sample from a discrete uniform distribution Find all IFoA past papers & memos at the following link: www.actuaries.org.uk/studying/prepare-your-exams/past-exam-papers-and-examiners-reports

Going through an IFoA past paper question regarding the normal approximation to the binomial as well confidence intervals using this approximation Find all IFoA past papers at the following link: www.actuaries.org.uk/studying/prepare-your-exams/past-exam-papers-and-examiners-reports

Going through an IFoA past paper question regarding the exact sampling distribution a discrete random variable and it's approximate sampling distribution using the Central Limit Theorem Find all IFoA past papers at the following link: www.actuaries.org.uk/studying/prepare-your-exams/past-exam-papers-and-examiners-reports

Going through an IFoA past paper question regarding the sampling distribution of the sampling variance. Find all IFoA past papers at the following link: www.actuaries.org.uk/studying/prepare-your-exams/past-exam-papers-and-examiners-reports

Overview of how the normal approximation is used for the binomial as well explaining and using the continuity correction.

Overview of the theory behind using the normal approximation to a binomial.

Explanation of the Central Limit Theorem and its use and importance in statistical inference.

Proof of the central limit theorem using MGFs

Walkthroughs of the sampling distributions of statistics related to the sample mean & variance, and how they related to the T Distribution and the F Distribution

Walkthroughs of the sampling distributions of the sample mean and variance for data that is normally distributed.

Proof that the sampling distribution of the sampling variance scaled by some important factor is a chi-squared distribution with n-1 degrees of freedom See PDF of all proofs here: bit.ly/YHH-Proofs

Proof: Sum of Independent Standard Normals is Chi-Square

Proof: Squared Standard Normal is Chi-Squared (Using MGF)

Proof: Squared Standard Normal is Chi-Squared (Using CDF)

Proof: Sample Mean is Normally Distributed

Topic Explainer: Statistical Inference & Sampling Distributions (Ch 7.1)