3. The random variable \(X\) has the discrete uniform distribution over the set of consecutive integers \(\{ - 7 , - 6 , \ldots , 10 \}\).
Calculate (a) the expectation and variance of \(X\),
(b) \(\mathrm { P } ( X > 7 )\),
(c) the value of \(n\) for which \(\mathrm { P } ( - n \leq X \leq n ) = \frac { 7 } { 18 }\).