{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

319handout5 - (b Find the probability that the lifetime of...

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

View Full Document Right Arrow Icon
Econ 319, Fall 2008 TA: Simon Kwok Handout 5 1. Suppose the probability density function (pdf) of the joint distribution of X and Y is given by: f ( x; y ) = ° C (2 x + 3 y ) ; 0 ° x; y ° 1 0 ; otherwise : (a) Find the value of C: (b) Find the marginal distributions of X and Y . Are X and Y independent? (c) Find the cumulative distribution functions (cdf) of X and Y: (d) Find the conditional distributions of X j Y and Y j X: (e) Find Pr( X + Y < 1) : (f) Find Pr( X + Y > 1 : 5) : 2. Suppose that the lifetime X (in 1000 hours) of a certain brand of lightbulb produced in a certain factory is distributed according to the following pdf: f ( x ) = ° Ce ° 1 2 x ; x > 0 0 otherwise. (a) Find the constant
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . (b) Find the probability that the lifetime of a lightbulb will be longer than 2000 hours. (c) Given that a lightbulb has been continuously lit for 2000 hours, what is the probability that it will last for at least another 2000 hours? (d) Suppose Simon bought 5 lightbulbs and he knows that their lifetimes are independently distributed. 1. What is the probability that at least one of them will burn out in less than 2000 hours? 2. What is the probability that more than two will burn out in less than 2000 hours? 1...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern