Let 'y' is a discrete variable taking values $y_1,y_2,y_3 ......y_n$ with probabilities $p_1, p_2, p_3......P_n$ respectively. Then standard deviation of 'y' is given by :

$\sqrt{E(y^2)-[E(y)]^2}$

The correct answer is option (2) → $\sqrt{E(y^2)-[E(y)]^2}$

Variance = $σ^2=E(Y^2)-[E(Y)]^2$

∴ Standard Deviation = $σ=\sqrt{E(y^2)-[E(y)]^2}$