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Q.

The random variable takes the values 1,2,3,…..,m. if $P (X = n) = \frac{1}{m}$ to each n, then the variance of X is

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a

$\frac{(m + 1) (2 m + 1)}{6}$

b

$\frac{m + 1}{2}$

c

$\frac{m^{2} + 1}{12}$

d

$\frac{m^{2} - 1}{12}$

answer is B.

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Detailed Solution

Mean $(μ) = \frac{m + 1}{2};$ Variance $(σ^{2}) = \frac{m^{2} - 1}{12}$

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