- (a) Explain briefly what is meant by a discrete random variable.
A family has 3 cats and 4 dogs. Two of the family's animals are to be chosen at random. The random variable \(X\) represents the number of dogs chosen.
(b) Copy and complete the table to show the probability distribution of \(X\) :
| \(x\) | 0 | 1 | 2 |
| \(\mathrm { P } ( X = x )\) | | | |
(c) Calculate
- \(\mathrm { E } ( X )\),
- \(\operatorname { Var } ( X )\),
- \(\operatorname { Var } ( 2 X )\).