A machine produces 0, 1 or 2 defective pieces in a day with

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

Let ‘x’ be no. of defective pieces.

Mean (μ) = E(x) = ∑ x P(x)

=		0 ×	1		+		1 ×	1		+		2 ×	1
			6					3					6

= 0 +	2	+	1	= 1
	3		3

E(x²) = ∑ x² P(x)

=		0 ×	1		+		1 ×	2		+		4 ×	1
			6					3					6

= 0 +	2	+	2	=	4
	3		3		3

Variance, V(x) = E(x²) – {E(x)}²

=	4	- 1 =	1
	3		3