Answer to a)

n = 1000 x = np.random.uniform(0, 1, n)

answer to b)

y = cot(-pi*x)

NEED HELP WITH C

a. [1 point] Use Python to generate the independent 1000 uniform random variables (say U1,..., U1000) on (0,1). (You should not print 1000 random variables in your report; Save time!). b. [2 points] Derive the inverse function F-) of the cumulative distribution function 3 F(x) f(z)dz= -+-arctan(z), z > 0 of the standard Cauchy random variable, that is, find the function F-1 which satisfies F-1 (F(x)) r for ER. [This part you do not use Python. If you work with Jupiter notebook, you can write explanations and derivations directly.] c Poinusingthe re preous problemgerateCahymriabes(..) ck :=F-1(U); in Python by k=1, , 1000 You do not need to print all the This method is called the inversion method