Correct Answer - Option 1 :
\(\frac{1}{{\sqrt {12} }}\)
Concept:
Standard deviation of a uniformly distributed random variable is given by:
F(x) = \(\left\{ {\begin{array}{*{20}{c}} {\frac{1}{{\beta - \alpha }}}\\ {\;else\;0\;\;\;} \end{array}} \right.\) If α < x < β,
Variance =\( \:\frac{{{{\left( {\beta - \alpha } \right)}^2}}}{{12}}\)
∴ Standard Deviation,
\(\;\sigma= \sqrt {\frac{{{{\left( {\beta\; - \;\alpha } \right)}^2}}}{{12}}\;} \;\)
Calculations:
Given:
β = 1, α = 0
Standard deviation of a uniformly distributed random variable is given by:
\(\;\sigma= \sqrt {\frac{{{{\left( {\beta\; - \;\alpha } \right)}^2}}}{{12}}\;} \;\)
\(\sigma {\rm{}} = {\rm{}}\sqrt {{\rm{\;}}\frac{{{{\left( {1 - 0} \right)}^2}}}{{12}}\;} \)
\(\sigma {\rm{\;}} = {\rm{}}\sqrt {{\rm{}}\frac{1}{{12}}\;} \)
\(\sigma {\rm{}} = {\rm{}}\frac{1}{{\sqrt {12} }}\)
Mean of a uniformly distributed random variable is given by:
Mean = \(\left(\frac{{\alpha \; + \;\beta }}{2}\right)\)
