4. The discrete random variable \(X\) has probability function \(\mathrm { P } ( X = x ) = k ( x + 4 )\). Given that \(X\) can take any of the values \(- 3 , - 2 , - 1,0,1,2,3,4\),

1. find the value of the constant \(k\).
2. Find \(\mathrm { P } ( X < 0 )\).
3. Show that the cumulative distribution \(\mathrm { F } ( x )\) is given by $$\mathrm { F } ( x ) = \lambda ( x + 4 ) ( x + 5 )$$ where \(\lambda\) is a constant to be found. \section*{STATISTICS 1 (A) TEST PAPER 4 Page 2}