3 The discrete random variable \(W\) has the distribution \(\mathrm { U } ( 11 )\). The independent discrete random variable \(V\) has the distribution \(\mathrm { U } ( 5 )\).
- It is given that, for constants \(m\) and \(n\), with \(m > 0\), \(\mathrm { E } ( \mathrm { mW } + \mathrm { nV } ) = 0\) and \(\operatorname { Var } ( \mathrm { mW } + \mathrm { nV } ) = 1\).
Determine the exact values of \(m\) and \(n\).
The random variable \(T\) is the mean of three independent observations of \(W\).
- Explain whether the Central Limit Theorem can be used to say that the distribution of \(T\) is approximately normal.