use downloaded software DrRacket, SCHEME program .scm , R5RS language from source. write SCHEME program .scm , language R5RS

1. [2 marks] Create a procedure (list->stream lis) that makes a stream from a given list.
2. [3 marks] Create a procedure (stream->list strm n) that makes a list from the first n items of the given stream.
3. [2 marks] Create a stream factorials that refers to the infinite stream of consecutive factorial values starting from 0! E.g. (stream-> list factorials 10) (1 1 2 6 24 120 720 5040 40320 362880)
4. [4 marks] A pseudo-random number generator (prng) can be defined using the following equation:

    Xn+1 = (a*Xn + c) mod m 

   • where m is the "modulus" (0 a is the "multiplier" (0 < a < m), c is the "increment" (0 c < m), and X₀ is the "seed" (0 X₀ < m) Using this formula, create a procedure called (prng seed) that takes a seed value as argument and produces an infinite stream of random numbers in the range [0,1). E.g.:

      (stream->list (prng 3) 5)  (0.01585 0.4954 0.9988 0.7253 0.0307) 

     Use the following values for the prng constants: m = 2³² a = 22695477 c = 1.0 Note: the equation above returns numbers in the range [0,m-1], you should ensure that your stream emits only numbers in the range [0,1)
5. [2 marks] Create a procedure (random-int r min max) that takes a stream of random numbers r in the range [0,1) and returns a stream of random integers in the range [min,max).