Exercise 1:

liste=Table[Random[Integer,{1,100}],{k,100}]

liste is a random list of integers between 1 and 100

(a)

Map[PrimeQ,liste]

List of the logical values, which tells whether the corresponding number of the list is prime or not.

(b)

Count[Map[PrimeQ,liste],True]

Number of the prime number of the list.

(c)

Map[(#^2)&,liste]

List of  square numbers of  liste.

(d)

Select[Map[Sqrt,liste],IntegerQ]

Liste of the numbers whose squarre are in liste.

(e)

N[Apply[Plus,liste]/Length[liste]]

Aritmetic average

(f)

Sqrt[Apply[Plus,Map[(#^2)&,liste]]]

Euklidian norm resp  length of the d"Vektor"  liste

(g)

Apply[Max,liste]

the maximum of the elements of  liste

e

Exercise 2

L=Table[Random[Integer,{-50,50}],{k,101}]

L´=If[PrimeQ[#],#,"false"]&/@L

L´´=Flatten[Position[L,x_/;PrimeQ[x]]]

L´´´=Select[L´,PrimeQ]