Mathematical Statistics Lecture [top] Jun 2026

for specific distributions. Explaining the Proofs for the Central Limit Theorem.

The final pillar of our lecture is hypothesis testing. This is the formal procedure for deciding between two competing claims: the null hypothesis and the alternative hypothesis. We use a test statistic to determine if the observed data is sufficiently extreme to warrant rejecting the null hypothesis. This process involves a delicate balance between Type I errors (false positives) and Type II errors (false negatives). The p-value, perhaps the most famous metric in statistics, tells us the probability of obtaining results at least as extreme as the ones observed, assuming the null hypothesis is true.

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Lectures teach you standard algorithmic ways to construct estimators from data. Maximum Likelihood Estimation (MLE)

Among unbiased estimators, we want the one with the smallest variance. for specific distributions

Hypothesis testing is a formal statistical framework used to make decisions about population parameters using sample data. The status quo, representing no effect or no difference. Alternative Hypothesis ( H1cap H sub 1 Hacap H sub a ): The claim the researcher wants to prove. Decision Matrix and Error Types Decision \ True State H0cap H sub 0 H0cap H sub 0 Reject H0cap H sub 0 Type I Error ( Correct Decision ( Fail to Reject H0cap H sub 0 Correct Decision ( Type II Error ( Significance Level (

Simple linear regression models the relationship between a dependent variable ( ) and an independent variable ( ) using a straight line: This is the formal procedure for deciding between

In advanced lectures, the focus shifts to the quality of our tools. You’ll explore:

The theory presented in these lectures is directly applied to critical, real-world sectors [5.1]: Clinical trials for new drug efficacy.