6. Use the sample formulas below to verify the following equations (a) - (g). \operatorname{Var}(X)=\frac{1}{n} \sum\left(X_{i}-\bar{X}\right)^{2} \operatorname{Cov}(X, Y)=\frac{1}{n} \sum\left(X_{i}-\bar{X}\right)\left(Y_{i}-\bar{Y}\right) \operatorname{Corr}(X, Y)=\frac{\operatorname{Cov}(X, Y)}{\sqrt{\operatorname{Var}(X) \operatorname{Var}(Y)}} \text { (a) } \operatorname{Var}(a X)=a^{2} \operatorname{Var}(X)

\text { (b) } \operatorname{Var}(a X+b)=a^{2} \operatorname{Var}(X) \text { (c) } \operatorname{Var}(a+b)=0 \text { (d) } \operatorname{Cov}(a X, b Y)=a b \operatorname{Cov}(X, Y) \text { (e) } \operatorname{Cov}(X, a)=0 \text { (f) } \operatorname{Cov}(X, Y+a)=\operatorname{Cov}(X, Y) \text { (g) } \operatorname{Corr}(a X, b Y)=\operatorname{Corr}(X, Y)