A box contains 6 pens, 2 of which are defective. Two pens are taken randomly from the box. If random variable x : Number of defective pens obtained, then standard deviation of x =

Question

A box contains 6 pens, 2 of which are defective. Two pens are taken randomly from the box. If random variable x : Number of defective pens obtained, then standard deviation of x =, ± 4 3 √ 5, 8 3, 16 45, 4 3 5

MARKS App · Accepted Answer

x : no. of defective pens Two pens are taken from box ∴ x can taken values 0, 1, 2 p x = 0 = 4 C 2 6 C 2 = 4 × 3 6 × 5 = 2 5 = 6 15 p x = 1 = 2 C 1 × 4 C 1 6 C 2 = 2 × 4 × 2 × 1 6 × 5 = 8 15 p x = 2 = 2 C 2 6 C 2 = 1 × 2 × 1 6 × 5 = 1 15 x P x i p i x i 2 p i 0 6 15 0 0 1 8 15 8 15 8 15 2 1 15 2 15 4 15 E x = 10 15 = 2 3 E x 2 = 12 15 = 4 5 Standard deviation = E x 2 - E x 2 Standard deviation = 4 5 - 2 3 2 = 4 5 - 4 9 = 4 × 4 45 = 4 3 √ 5

x	P	$x_{i} p_{i}$	$x_{i}^{2} p_{i}$
0	$\frac{6}{15}$	0	0
1	$\frac{8}{15}$	$\frac{8}{15}$	$\frac{8}{15}$
2	$\frac{1}{15}$	$\frac{2}{15}$	$\frac{4}{15}$

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