write a short MATLAB script to implement the above algorithm and generate 10,000 samples of the random variable S. Plot a histogram of the obtained distribution and, on the same set of axes, include a plot of the normal density function (use normfit function). Compute the empirical mean and variance of the distribution (use mean and var functions). Comment on the accuracy of this approach to generate samples from the normal distribution.

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?