The first critical concept in any mathematical statistics lecture is the notion of a statistical model. We typically assume that our data points are realizations of independent and identically distributed random variables. These variables follow a distribution characterized by one or more parameters, denoted by the Greek letter theta. Our primary goal is to use the sample data to make statements about this unknown parameter.
The most important theorem in statistics: mathematical statistics lecture
Learning how to find a single "best guess" value. You will dive deep into the Method of Moments and Maximum Likelihood Estimation (MLE) —the latter being a cornerstone of modern data science. The first critical concept in any mathematical statistics
An estimator is consistent if it converges in probability to the true parameter as the sample size $n \to \infty$. $$\hat\theta_n \xrightarrowP \theta$$ (As we get more data, the estimate gets arbitrarily close to the truth). Our primary goal is to use the sample
As the bell rang, the students packed their bags, no longer just looking at numbers, but at the invisible patterns hidden in the chaos of the world. Aris watched them go, knowing that by next week, half of them would still be confused by p-values , but at least they knew the ghost was there.
$$\fracn\lambda = \sum_i=1^n x_i \implies \lambda = \fracn\sum x_i$$ $$\hat\lambda_MLE = \frac1\barX$$ (This makes sense; the rate parameter $\lambda$ is the inverse of the average time).