1
| \(S\) |
| 0 | 1 | 2 |
| 0 | \(\frac { 1 } { 8 }\) | \(\frac { 1 } { 8 }\) | 0 |
| 1 | \(\frac { 1 } { 8 }\) | \(\frac { 1 } { 4 }\) | \(\frac { 1 } { 8 }\) |
| 2 | 0 | \(\frac { 1 } { 8 }\) | \(\frac { 1 } { 8 }\) |
An unbiased coin is tossed three times. The random variables \(F\) and \(S\) denote the total number of heads that occur in the first two tosses and the total number of heads that occur in the last two tosses respectively. The table above shows the joint probability distribution of \(F\) and \(S\).
- Show how the entry \(\frac { 1 } { 4 }\) in the table is obtained.
- Find \(\operatorname { Cov } ( F , S )\).