\text { Use the definitions } \bar{X}=\frac{1}{n} \sum X_{i} \text { and } s_{X}^{2}=\frac{1}{n} \sum\left(X_{i}-\bar{X}\right)^{2} \text { to show that if } Y_{i}= a + bX¡, then \text { (a)

} \bar{Y}=a+b \bar{X} \text { and } s_{Y}^{2}=\frac{1}{n} \sum\left(Y_{i}-\bar{Y}\right)^{2}=b^{2} s_{X}^{2} \text { (b) If } Z_{i}=\frac{X_{i}-\bar{x}}{6_{x}}, \text { then } \bar{Z}=0 \text { and } s_{Z}^{2}=1