The distribution function of the random vector (left(xi_{1}, xi_{2}, ldots, xi_{n} ight)) is (Fleft(x_{1} ight.), (left.x_{2}, ldots,

 The distribution function of the random vector \(\left(\xi_{1}, \xi_{2}, \ldots, \xi_{n}\right)\) is \(F\left(x_{1}\right.\), \(\left.x_{2}, \ldots, x_{n}\right)\). As the result of a trial the components of the vector take on the values \(\left(z_{1}, z_{2}, \ldots, z_{n}\right)\). Find the distribution function of the random variable:

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

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