Question

Variance of 1, 3, 5, 7......... (4n + 1) is ________

(a) [{2n(2n – 1)}/3]

(b) √[(n + 1)/{3(n – 1)}]

(c) (1/n) √[(n² – 1)/3]100

(d) [{4n(n + 1)}/3]

Answer 1

The correct option (d) [{4n(n + 1)}/3]  

Explanation:

Variance of 1, 2, 3 ......... m = [(m² – 1)/12]

Let yi = 2xi – 1

∴ S²y = 4S²x

∴ S²y = 4[(m² – 1)/12] 

Here take m = 2n + 1

∴ Variance of 1, 3, 5,......... (4n + 1)

= S²y = (4/12)[(2n + 1)² – 1]

= (1/3)[4n(n + 1)].