For the following distribution : X 1 2 3 4 P(X) 1/10 1/5 3/10 2/5 Var…

The correct answer is Option (3) → 1

$E(X)=1×\frac{1}{10}+2×\frac{1}{5}+3×\frac{3}{10}+4×\frac{2}{5}=3$

$E(X^2)=1^2×\frac{1}{10}+2^2×\frac{1}{5}+3^2×\frac{3}{10}+4^2×\frac{2}{5}=10$

So $Var(X)=E(X^2)-E^2(X)$

$=10-3^2=1$