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

$$\text{Suppose }Y_i \overset{iid}{\sim} N\left(0, 1^2 \right)$$

$$\bar Y \sim N(\mu, {\sigma^2\over{n}})$$

$$\text{Hence, } Z = { {\bar Y - \mu} \over {\sigma / \sqrt{n}}} \sim N (0, 1)$$