## Mathematical Statistics

created : 2020-04-07T11:48:25+00:00
modified : 2020-10-16T15:01:38+00:00

# Chapter 7 Sampling distribution

## Definition 7.1 (Statistic)

• A statistic is a function of the observations in a sample and known constants. The distribution of a statistic is called the sampling distribution of the statistic.
$\bar Y: \text{sample mean}$ $S^2 : \text{sample variance}$ $Y_{(1)}, Y_{(n)} : \text{minimum and maximum (order statistics)}$ $\hat p : \text{sample proportion}$

## Theorem 7.1

$\text{Suppose }Y_i \overset{iid}{\sim} N\left(0, 1^2 \right)$ $\bar Y \sim N(\mu, {\sigma^2\over{n}})$ $\text{Hence, } Z = { {\bar Y - \mu} \over {\sigma / \sqrt{n}}} \sim N (0, 1)$