Question Type 8: For given values of either summary statistic, finding another corresponding value using properties Exercises

Given $E(X)=5$, $E(Y)=-1$, and $\text{Cov}(X,Y)=2$, find $E(XY)$.

Given $\text{Var}(X)=4$, find the standard deviation of $0.5X$.

Given $E(X)=1$ and $E(Y)=2$, find $E(4X - 5Y + 3)$.

Given $\text{E}(X)=-3$ and $\text{Var}(X)=2$, find $\text{Var}(X + 5)$.

Given $E(X)=0.7$ and $E(X^2)=0.9$, find $\text{Var}(2X)$.

Given $\text{Var}(X)=6$, $\text{Var}(Y)=9$ and $\text{Cov}(X,Y)=5$, find $\text{Cov}(2X - Y, 3X + 4Y)$.

Given $\text{Var}(X)=9$, $\text{Var}(Y)=16$, and $\text{Cov}(X,Y)=6$, find $\text{Var}(2X - 3Y)$.

Given $\operatorname{E}(X)=0$ and $\operatorname{Var}(X)=1$, find $\operatorname{Var}\left(\frac{X+2}{3}\right)$.

Given $E(X)=2$ and $\text{Var}(X)=3$, find $E(X^2)$.

Given $E(X)=5$, find $E(3X - 2)$.

Given $\text{Var}(X)=9$, $\text{Var}(Y)=16$, and $\text{Cov}(X,Y)=6$, find $\text{Var}(X+Y)$.

Given $\text{Var}(X)=4$, find $\text{Var}(3X + 1)$.