1 A discrete random variable \(X\) has the following distribution, where \(a , b\) and \(c\) are constants.
| \(x\) | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( \mathrm { X } = \mathrm { x } )\) | \(a\) | \(b\) | \(c\) | 0.1 |
It is given that \(\mathrm { E } ( X ) = 1.25\) and \(\operatorname { Var } ( X ) = 0.8875\).
- Determine the values of \(a\), \(b\) and \(c\).
- The random variable \(Y\) is defined by \(Y = 7 - 2 X\).
Write down the value of \(\operatorname { Var } ( Y )\).
- Twenty independent observations of \(X\) are obtained. The number of those observations for which \(X = 3\) is denoted by \(T\).
Find the value of \(\operatorname { Var } ( T )\).