Tag critical value

Confidence Intervals For The Variance and Standard Deviation of a Normal Distribution

\(\newcommand{\Cov}{\mathrm{Cov}}\) \(\newcommand{\Corr}{\mathrm{Corr}}\) \(\newcommand{\Sample}{X_{1},\dots,X_{n}}\) Let \(\Sample\) be...

A Prediction Interval for a Single Future Value For a Normal Distribution

What if you have \(n\) observations in a normal distribution and want to predict \(X_{n+1}\)? The prediction interval is \(\bar{x}\pm...

Intervals Based on a Normal Population Distribution: The T-Distribution

Say you take a sample where \(n\) is not large. Then the CLT doesn’t apply. We must then know/assume a distribution. Suppose we know it...

Basic Properties of Confidence Intervals

\(\newcommand{\Cov}{\mathrm{Cov}}\) \(\newcommand{\Corr}{\mathrm{Corr}}\) \(\newcommand{\Sample}{X_{1},\dots,X_{n}}\) Assume you have a...

The Normal Distribution

Probability Distribution Function The parameters are \(-\infty<\mu<\infty\) and \(\sigma>0\). \begin{equation*}...