3 The random variable \(X\) represents the value on the upper face of an eight-sided dice after it has been rolled. The faces are numbered 1 to 8 The random variable \(X\) is modelled by a discrete uniform distribution with \(n = 8\)
3

1. Find \(\mathrm { E } ( X )\)
   3
2. \(\quad\) Find \(\operatorname { Var } ( X )\)
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3. Find \(\mathrm { P } ( X \geq 6 )\)
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4. The dice was rolled 800 times and the results below were obtained.

   \(\boldsymbol { x }\)	\(\mathbf { 1 }\)	\(\mathbf { 2 }\)	\(\mathbf { 3 }\)	\(\mathbf { 4 }\)	\(\mathbf { 5 }\)	\(\mathbf { 6 }\)	\(\mathbf { 7 }\)	\(\mathbf { 8 }\)
   Frequency	103	63	84	110	74	41	85	240

   State, with a reason, how you would refine the model for the random variable \(X\).
   [0pt] [2 marks]