Let X be a discrete random variable whose probability distribution is defined as follows: $$P(X=x)=\left \{\begin{array}{1 1}k(x+1) & for\;x=1,2,3,4\\2kx & for\;x=5,6,7\\0 & otherwise\end{array} \right.$$ where k is a constant. Calculate $$(i)\;the\;value\;of\;k\quad(ii)\;E(X)\quad(iii)\;standard\;deviation\;of\;X$$

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