IB Mathematics Analysis and Approaches 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 $E(X)=0$ and $\mathrm{Var}(X)=1$, find $\mathrm{Var}\left(\frac{X+2}{3}\right)$.

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 $\text{Var}(3X+1)$.