2 The probability distribution for the discrete random variable \(W\) is given in the table.
| \(w\) | 1 | 2 | 3 | 4 |
| \(\mathrm { P } ( W = w )\) | 0.25 | 0.36 | \(x\) | \(x ^ { 2 }\) |
- Show that \(\operatorname { Var } ( W ) = 0.8571\).
- Find \(\operatorname { Var } ( 3 W + 6 )\).
In this question you must show detailed reasoning.
The random variable \(T\) has a binomial distribution. It is known that \(\mathrm { E } ( T ) = 5.625\) and the standard deviation of \(T\) is 1.875 . Find the values of the parameters of the distribution.