Functions (Plot) The aim is to fill two vector arrays xv and yv with x and f(x) values, respectively, where the probability density function for Pareto is: (,)=+1 f ( x , b ) = b x b + 1 for >1 x > 1 and >0 b > 0 . Pareto takes b as a shape parameter for b . Let the x v values be uniformly spaced in =[1,5] x v = [ 1 , 5 ] with 100 grid points. Write a loop to fill in the values for x v and =(,) y v = f ( x v , b ) , for =1 b = 1 , =2 b = 2 and =3 b = 3 . So at the end you should have a vector x v with the X-values and a vector y v with the function values (,) f ( x , b ) for any given b . Plot y v against x v using the plot command (you should have three lines in a single figure - one for each b ).

Exercise 9 (4(x-1)). Consider the following function: f(x) = sin( 4 for x (0,2). 1. Plot the function. 2. Find the value of x such that f(x) = 0 using the Newton-Raphson homemade function provided. 3. Use Newton's optimization method available in the scipy.optimize library. 4. Use the built in function fmin is in the scipy.optimize library. Exercise 9 (4(x-1)). Consider the following function: f(x) = sin( 4 for x (0,2). 1. Plot the function. 2. Find the value of x such that f(x) = 0 using the Newton-Raphson homemade function provided. 3. Use Newton's optimization method available in the scipy.optimize library. 4. Use the built in function fmin is in the scipy.optimize library