Question

The probability distribution of X, the number of defects per 10 metres of a fabric is given by

x	0	1	2	3	4
P(X = x)	0.45	0.35	0.15	0.03	0.02

Find the variance of X

 

Answer 1

xi	pi	`p_ix_i`	`p_ix_i^2`
0	0.45	0	0
1	0.35	0.35	0.35
2	0.15	0.30	0.60
3	0.03	0.09	0.27
4	0.02	0.08	0.32
Total		0.82	1.54

From the table, `sum p_ix_i` = 0.82 and `sum p_ix_i^2` = 1.54

∴ Var(X) = `sump_ix_i^2 - (sump_ix_i)^2`

= 1.54 − (0.82)²

= 1.54 − 0.6724

∴ Var (X) = 0.8676