Let X be a distance random variable whose probability distribution is defined as :

$P(X=x)= \left\{\begin{matrix}0.5 & ,if & x=0\\k(x+1) & ,if & x=1\, or \, 2\\k(6-x) & ,if & x=3\, or\, 4\\0 & , & otherwise\end{matrix}\right.$

The, value of k is :

$\frac{1}{20}$