4 The discrete random variable \(X\) follows a discrete uniform distribution and takes values \(1,2,3 , \ldots , n\).
The discrete random variable \(Y\) is defined by \(Y = 2 X\)
4
- Using the standard results for \(\sum n , \sum n ^ { 2 }\) and \(\operatorname { Var } ( a X + b )\), prove that
$$\operatorname { Var } ( Y ) = \frac { n ^ { 2 } - 1 } { 3 }$$
4
- A spinning toy can land on one of four values: 2, 4, 6 or 8
Using a discrete uniform distribution, find the probability that the next value the toy lands on is greater than 2
4 - State an assumption that is required for the discrete uniform distribution used in part (b) to be valid.