Dr. Hackney STA Solutions pg 47

Dr. Hackney STA Solutions pg 47 - Second Edition 4-3 1 V 2...

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

View Full Document Right Arrow Icon
Second Edition 4-3 U 1 2 3 2 1 12 1 6 1 12 V 3 1 12 1 6 1 12 4 1 12 1 6 1 12 4.11 The support of the distribution of ( U, V ) is { ( u, v ) : u = 1 , 2 , . . . ; v = u + 1 , u + 2 , . . . } . This is not a cross-product set. Therefore, U and V are not independent. More simply, if we know U = u , then we know V > u . 4.12 One interpretation of “a stick is broken at random into three pieces” is this. Suppose the length of the stick is 1. Let X and Y denote the two points where the stick is broken. Let X and Y both have uniform(0 , 1) distributions, and assume X and Y are independent. Then the joint distribution of X and Y is uniform on the unit square. In order for the three pieces to form a triangle, the sum of the lengths of any two pieces must be greater than the length of the third. This will be true if and only if the length of each piece is less than 1 / 2. To calculate the probability of this, we need to identify the sample points ( x, y ) such that the length of each piece is less than 1 / 2. If y > x , this will be true if x < 1 / 2, y - x < 1 / 2 and 1 - y < 1 / 2.
Image of page 1
This is the end of the preview. Sign up to access the rest of the 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