- The discrete random variable \(Y\) has the following probability distribution
| \(y\) | - 9 | - 5 | 0 | 5 | 9 |
| \(\mathrm { P } ( Y = y )\) | \(q\) | \(r\) | \(u\) | \(r\) | \(q\) |
where \(q , r\) and \(u\) are probabilities.
- Write down the value of \(\mathrm { E } ( Y )\)
The cumulative distribution function of \(Y\) is \(\mathrm { F } ( y )\)
Given that \(F ( 0 ) = \frac { 19 } { 30 }\) - show that the value of \(u\) is \(\frac { 4 } { 15 }\)
Given also that \(\operatorname { Var } ( Y ) = 37\)
- find the value of \(q\) and the value of \(r\)
The coordinates of a point \(P\) are \(( 12 , Y )\)
The random variable \(D\) represents the length of \(O P\)
- Find the probability distribution of \(D\)