The probability distribution of a discrete random variable is given by : $P(X-x)=\left\{\begin{matrix} 3kx & for & x=1, 2,3 \\2k(x+3) & for & x=4, 5, 6\\0 & & otherwise \end{matrix}\right.$ where k is a constant. The mean of X is :

$\frac{13}{3}$ $\frac{5}{3}$ 2.5 $\frac{10}{3}$

$\frac{13}{3}$