# HW5 - X(b The manufacturer sells the article for a ﬁxed...

This preview shows page 1. Sign up to view the full content.

OR 3500/5500, Summer’09, Chen Homework 5 Due on Wednesday, June 3, 3:00pm. Problem 1 In a population on size 100, 20 are smoker. A random sample of size 5 is chosen without replacement. Let X denote the number of smokers in the sample. Compute Var( X ). Hint: Define suitable indicator random variables. Problem 2 Let X and Y have a joint pdf given by f X,Y ( x, y ) = 1 if 0 < y < 1 , y - 1 < x < 1 - y 0 otherwise . (a) Find Cov( X, Y ) and ρ X,Y . Are X and Y independent? (b) Find Cov( | X | , | Y | ) and ρ | X | , | Y | . (c) Find Cov(3 | X | , 4 | Y | ) and ρ 3 | X | , 4 | Y | . (d) Find Var(3 X - 2 Y ). Problem 3 A random variable X , which represents the weight (in ounces) of an article, has density function given by f X ( x ) = x - 8 for 8 x 9 10 - x for 9 < x 10 0 otherwise . (a) Calculate the mean and variance of the random variable
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X (b) The manufacturer sells the article for a ﬁxed price of \$2 . 00. He guarantees to refund the purchase money to any customer who ﬁnds the weight of his article to be less than 8 . 25 oz. His cost of production is related to the weight of the article by x/ 15 + . 35. Find the expected proﬁt per article and its standard deviation. The following problem is optional for 3500 students, mandatory for students enrolled in 5500 Problem 4 Let p i = P ( X = i ) and suppose that p 1 + p 2 + p 3 = 1. If EX = 2, what values of p 1 ,p 2 and p 3 ( a ) maximize and ( b ) minimize Var X ? 1...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern