Question

6E(X²) - V(X) =

X	-1	0	1	2
P(X)	1/3	1/6	1/6	1/3

• A. 23/36
• B. 47/12
• C. 1/6
• D. 113/12

Answer 1

Answer:

D. 113/12

$E(X)=ΣxP(x)$

$E(X)= \frac{-1}{3}+\frac{1}{6}+\frac{2}{3} = \frac{1}{2}$

$E(X^2)=Σx^2P(x)$

$E(X^2)=\frac{1}{3}+\frac{1}{6}+\frac{4}{3} = \frac{11}{6}$

$V(X)= E(X^2)-[E(X)]^2$

$V(X) = \frac{11}{6}- (\frac{1}{2})^2 = \frac{19}{12}$

$6E(X^2) - V(X) = 6 \times \frac{11}{6} - \frac{19}{12} = \frac{113}{12}$