COMP 2711 Ex 12

1

a

$$\begin{array}{rl}E(X)& =\frac{1+2+3+4+5+6}{6}\\ & =\frac{7}{2}\\ V(X)& =\frac{{\left(1-\frac{7}{2}\right)}^2+{\left(2-\frac{7}{2}\right)}^2+{\left(3-\frac{7}{2}\right)}^2+{\left(4-\frac{7}{2}\right)}^2+{\left(5-\frac{7}{2}\right)}^2+{\left(6-\frac{7}{2}\right)}^2}{6}\\ & =\frac{35}{12}\end{array}$$

b

$$\begin{array}{rl}& E(2X)=2\cdot \frac{7}{2}=7\\ & V(2X)=2^2\cdot \frac{35}{12}=\frac{35}{3}\end{array}$$

c

$$\begin{array}{rl}& E(X+Y)=\frac{7}{2}+\frac{7}{2}=7\\ & V(X+Y)=\frac{35}{12}+\frac{35}{12}=\frac{35}{6}\end{array}$$