Question 4: Properties of Random Number Generators Which of the following statements are correct about random number generators? (a) For a good random number generator, the period is small. (b) Python's np. random. rand() is a pseudo random number generator. (C) Successive values appear to be independent with a good random number generator. (d) Python's np. random. rand() uses counter-based random number generation. Select all possible options that apply. Save & Grade Save only Question 6: Taylor Polynomials If f(x) = (3x 15)-(4x2 20x + 50), which of the following statements are true? Note: The remainder term is given by Rn(x) = Tn(x) f(x) where Tn(x) is the degree n Taylor expansion with center 0. (a) The magnitude of the remainder term R5(1) for Taylor series expansion around 0 of f(x) is equal to 1440. (b) The magnitude of the remainder term R6(1) for Taylor series expansion around 0 of f(a) is equal to 6. (c) The magnitude of the remainder term R5(1) for Taylor series expansion around 0 of f(x) is equal to 144. (d) The Taylor polynomial of degree 6 about x = 10 for f(x) is equal to f(a). (e) The Taylor polynomial of degree 6 about x = 10 for f(x) is NOT equal to f(x). (f) The magnitude of the remainder term R6(1) for Taylor series expansion around 0 of f(x) is equal to zero. Select all possible options that apply