- The discrete random variable \(X\) can take only the values \(1,2,3\) and 4 . For these values, the probability function is given by
$$\mathrm { P } ( X = x ) = \frac { a x + b } { 60 } \quad \text { for } x = 1,2,3,4$$
where \(a\) and \(b\) are constants.
- Show that \(5 a + 2 b = 30\)
Given that \(\mathrm { F } ( 3 ) = \frac { 13 } { 20 }\)
- find the value of \(a\) and the value of \(b\)
Given also that \(Y = X ^ { 2 }\)
- find the cumulative distribution function of \(Y\)