The discrete random variable \(X\) has probability distribution,
\(x\)
- 1
0
1
3
7
\(\mathrm { P } ( X = x )\)
\(p\)
\(r\)
\(p\)
0.3
\(r\)
where \(p\) and \(r\) are probabilities.
Given that \(\mathrm { E } ( X ) = 1.95\)
find the exact value of \(\mathrm { E } ( \sqrt { X + 1 } )\) giving your answer in the form \(a + b \sqrt { 2 }\) where \(a\) and \(b\) are rational.
(6)