Distribution of a finite random variable
The sample space \(S\) contains the ordered outcomes of a finite 2-stage experiment
At the first stage, the possible outcomes are absent, present. Their numerical codes, in the same order, are 0, 1
At the second stage, the possible outcomes are absent, present. Their numerical codes, in the same order, are 0, 1
The exact probabilities of the ordered outcomes are given below. Outcomes from successive stages remain ordered
| Ordered outcome | Exact probability |
|---|---|
| (absent, absent) | 4/15 |
| (absent, present) | 1/3 |
| (present, absent) | 1/3 |
| (present, present) | 1/15 |
Define \(X\) as the number of stages whose outcome is absent
The possible values of \(X\) are \(\{0,\,1,\,2\}\)