# Given the following probability distribution, $\begin{matrix} \text{X} & 0 &1 &2 &3&4&5&6&7\\ \text{P(X)}&0&k&2k&2k&3k&k^2&2k^2&7k^2+k \end{matrix}$ determine $\;(i) k\quad (ii) P(X \lt 3)\quad (iii) P(X \gt 6)\quad (iv) P(0 \lt X \lt 3)$
$\begin{array}{1 1}(i) .10, (ii) .30, (iii) .17, (iv) .30 \\ (i) .10, (ii) .20, (iii) .07, (iv) .30 \\(i) .05, (ii) .30, (iii) .17, (iv) .20 \\ (i) .05, (ii) .30, (iii) .07, (iv) .20 \end{array}$