Text Book Problem Numbers

Instructions
Homework 6
Chapter 3, Sections 3.5, 3.6, 3.7
Text Book Problem Numbers
Section 3-5

1. Do problem 3-5.1 in the text.
2. Do problem 3-5.5 in the text part (a) and (c) only.
3. Do problem 3-5.6 in the text.
   Section 3-6 (These problems are not from the book chapter 3 selection)
4. We are given two functions;
   V = g(x,y) = 3X + 5Y
   W = h(x,y) = X + 2Y.
   The joint PDF of RV X and Y is given as fxy(x,y)=exp[-1/2(x2+y2
   )]. What is the joint PDF of the
   two new RVs V=g(X,Y) and W=h(X,Y)?
5. Consider two RVs X and Y with joint PDF fxy(x,y). Determine the PDF of Z if Z=X/Y
   and W=Y.
   Section 3-7
6. Do problem 3-7.1 in the text
7. Do problem 3-7.4 in the text
8. Do problem 3-7.5 in the text
   MATLAB Assignment: (6 points)
   Matlab Problem HW 6
   In matlab add ‘L’ independent uniformly distributed random
   variables using the code below. Z=X1+X2+X3+…XL.
   From the resulting sum of the L random variables, you can use
   the code below to plot the probability mass function.
9. What is the distribution of the RV Z? Plot out your
   probability mass function. Comment on the type of
   distribution you anticipate based on the principles of the
   Central Limit Theorem.
10. Use the lillietest.m function to test for your anticipated
    distribution.
11. How many random variables (setting of the input variable L)
    must me added before the distribution converges to the
    distribution consistent with the principles of the Central
    Limit Theorem? Demonstrate this with the test in b.) above.
    Show all your work and code as well as the output of your
    code.
    %%%%%%% Matlab Assignment for HW # 6 %%%%%%%%
    close all, clear all
    N=10000;
    L=2; % input the number of RV to be %summed
    z=zeros(1,N);
    for i=1:L
    x=2*(-.5+rand(1,N));
    z=z+x;
    end
    %%%%%%% PMF of RV Z with 20 statitical bins in the range of X
    [m,zz]=hist(z,20); %counts samples of X in each bin and provides
    bin coordinates
    mm=m/(N); % computes the probability in each bin
    subplot(1,2,2);bar(zz,mm) % plot normalized histigram (PMF)
    xlabel('Random Variable Z')
    ylabel('Probability Mass Function')