Question

A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

• A. 1 and 1/3
• B. 1/3 and 1
• C. 1 and 4/3
• D. 1/3 and 4/3

Answer 1

The correct option is A 1 and 1/3

Mean, $\mu =E\left(x\right)$

$=\sum xp\left(x\right)$

$=0\times \frac{1}{6}+1\times \frac{2}{3}+2\times \frac{1}{6}=1$

Variance,
$V=E\left(x^2\right)-\left[E\right(x){]}^2$

$=\sum x^{2}p\left(x\right)-1^2$

$=0^2\times \frac{1}{6}+1^2\times \frac{2}{3}+2^2\frac{1}{6}-1$

$V=\frac{4}{3}-1$

$V=\frac{1}{3}$