A total of \(n\) independent trials are performed on a random variable \(\xi\) having a continuous distribution function, as a result of which the following vaiues of the variable \(\xi\) were observed: \(x_{1}, x_{2}, \ldots, x_{n}\). Find the distribution functions of the random variables:

(a) \(\eta_{n}=\max \left(x_{1}, x_{2}, \ldots, x_{n}\right)\);

(b) \(\zeta_{n}=\min \left(x_{1}, x_{2}, \ldots, x_{n}\right)\)

(c) the \(k\) th largest observation result;

(d) the joint distribution of the \(k\) th ' and \(m\) th largest observed values.