Montgomery College Rockville Campus Central Theorem Limit Matlab Task

1 I


Need a custom paper ASAP?
We can do it today.
Tailored to your instructions. 0% plagiarism.


One of the most important theorems in the study of probability and random processes is the Central Limit Theorem

(CLT). Let us define the sample sum of independent random variables, ,where each random variable,

, has a finite mean, , and a finite variance, . The Central Limit Theorem states that in this case, has a

probability density function (pdf) that approaches a Gaussian pdf with mean and a variance

as grows large (but not infinite!).

Put it this way: if we add a bunch of well-behaved independent random variables together, the pdf of the sum is

approximately Gaussian, and the approximation gets better as we add more terms (i.e., more independent random

variables) to the sum. The approach to Gaussian in the limit as N gets large does not depend on the shape of the

pdfs, or even on the random variables being identically distributed. All that is required is that they are


We will study the CLT during the course of this project, but you do not need to wait for us to cover it in class. You

can do all of the project without us discussing the CLT in class.

Warning #1: Thinking is required!

Warning #


: Follow directions!

Warning #3: It isn’t on the web, so don’t bother looking.


Perform the following tasks, then document your results and submit them in written form in accordance with the

instructions in Section 3, below. You may (and should) use this document as a template for your report.

2.1 Sum of Independent, Identically Distributed (iid) Random Variables from U(0,1)

Generate the sum of N random variables distributed for .

MATLAB users will use the function rand.

Generate a large number of such sums, say 100,000 or more, for each value of . Plot a histogram of the results

for each , scaling the histogram appropriately to be a probability density function. (Note that the random variable

upon which the histogram is based is the sum of N random variables, and there are a large number of such sums in

each experiment. See the MATLAB skeleton for some hints.) In each case, compute the mean and standard

N Y =




Xk mk


s k Y

m = mk


∑ σ2 = σ k


Xk ~ U(0,1),k = 1,2…,N NNN === 2, 6, 12


Place your order
(550 words)

Approximate price: $22

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
The price is based on these factors:
Academic level
Number of pages
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
Live Chat+1(978) 822-0999EmailWhatsApp

Order your essay today and save 20% with the discount code LEMONADE