Question

2. Let X have mean 2 and variance 9. (a) What is the mean and variance of 5-3X? (b) What is the mean and variance of (X - 2)/3? (c) What is the mean and variance of (5X - 10)/2?

Answer 1

X have mean 2 and variance 9

a)

E(5-3x) = 5 - 3 *E(x) = 5-3*2=-1

V(5-3x) = V(-3x)

=9*V(x)

=9*9

=81

b)

$E(\frac{x-2}{3})=\frac{1}{3}E(x-2)=\frac{1}{3}\left ( E(x)-2 \right )=\frac{1}{3}\left ( 2-2 \right )=0$

$V(\frac{x-2}{3})=\frac{1}{9}V(x-2)=\frac{1}{9}*9=1$

c)

$E(\frac{5x-10}{2})=\frac{1}{2}E(5x-10)=\frac{1}{2}\left (5* E(x)-10 \right )=\frac{1}{2}\left ( 5*2-10 \right )=0$

$V(\frac{5x-10}{2})=\frac{1}{4}V(5x-10)=\frac{25}{4}*9=56.25$