5 In a particular discrete probability distribution the random variable \(X\) takes the value \(\frac { 120 } { r }\) with probability \(\frac { r } { 45 }\), where \(r\) takes all integer values from 1 to 9 inclusive.
- Show that \(\mathrm { P } ( X = 40 ) = \frac { 1 } { 15 }\).
- Construct the probability distribution table for \(X\).
- Which is the modal value of \(X\) ?
- Find the probability that \(X\) lies between 18 and 100 .