Question

Instructions: If you require uniformly distributed random numbers
in [0, 1], use Matlab’s built in uniform random number generator rand. Also,
you may NOT use any Matlab built-in functions that explicitly perform the task
asked for in the problem.

Problem 6. Let α > 0 and set f(x)- ae-ale, for x e(-oo, oo). (a) Make a plot of f (b) Show that f is a probability density function (Hint: -, when z S 0, and x-r, when 0.) (c) If X ~ f, find the cumulative distribution function. F for X given by F(x)-P(X < r). (d) Make a plot of F. (d) Find F-(u). for u E (0,1) by solving the equation u = F(r) for r. (Hint: Consider 0 < u anj u < 1 separately. )(e) Make a plot of F-1(u). (f) Choose a value for α > 0 and write a Matlab function that samples X g) Call the function you wrote in Part (f) to make a Histogram of samples of X. Problem 7. (a) Use Problem 6 above with an appropriate choice of a > 0, the Matlab function rand, and Rejection Sampling as explained in class to write a Matlab function that generates samples from the standard normal, Z (b) Check that your function in Part (a) is correct by calling it a large number of times and make a histogram. (c) Use the function you wrote in part (a) to write a function that generates samples from a normal distribution with mean ,1 and standard deviation ơ. The input to your function should be values for μ and σ. (Hint: This part is actually trivial!) (d) Check that your function in Part (c) is correct by calling it a large number of times and make a histogram.

Answer 1

Problem 6 ズEP- ko) α且 ブ·人。 咚. ズ70

As per HomeworkLib policy we only have authority to post answers to the first 4 subparts of a question