3 John has a standard die in his pocket (ie a cube with its six faces labelled from 1 to 6).
- Describe how John can use the die to obtain realisations of the random variable \(X\), defined below.
| \(x\) | 1 | 2 | 3 |
| \(\operatorname { Probability } ( X = x )\) | \(\frac { 1 } { 2 }\) | \(\frac { 1 } { 6 }\) | \(\frac { 1 } { 3 }\) |
- Describe how John can use the die to obtain realisations of the random variable \(Y\), defined below.
| \(y\) | 1 | 2 | 3 |
| \(\operatorname { Probability } ( Y = y )\) | \(\frac { 1 } { 2 }\) | \(\frac { 1 } { 4 }\) | \(\frac { 1 } { 4 }\) |
- John attempts to use the die to obtain a realisation of a uniformly distributed 2-digit random number. He throws the die 20 times. Each time he records one less than the number showing. He then adds together his 20 recorded numbers.
Criticise John's methodology.