NotesSep13 - Example When a certain method is used to...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Example When a certain method is used to collect a fixed volume of rock samples in a region, there are 4 rock types. Let X 1 , X 2 and X 3 be the proportions by volume of the first 3 rock types in randomly selected sample. Based on empirical data, X 1 , X 2 , X 3 are mod- eled as a continuous random vector with a joint pdf f X 1 ,X 2 ,X 3 ( x 1 , x 2 , x 3 ) = 144 x 1 x 2 (1 - x 3 ) for x 1 > 0 , x 2 > 0 , x 3 > 0 and 0 < x 1 + x 2 + x 3 < 1. Find the probability that rocks of type 1 and 2 together account for at most 50% of the volume of the sample.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Independent Random Variables Independent random variables are such that, knowing the value of one of them, does not tell us anything about the values of the rest. Formally, random variables X 1 , . . . , X n are in- dependent if for all sets A 1 , . . . , A n P ( X 1 A 1 , . . . , X n A n ) = P ( X 1 A 1 ) . . . P ( X n A n ) = n Y j =1 P X j A j .
Image of page 2
Criteria for independence Random variables X 1 , . . . , X n are indepen- dent if and only if the joint cdf factors out into a product of the marginal cdfs: F X 1 ,...,X n ( x 1 , . . . , x n ) = P ( X 1 x 1 , . . . , X n
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
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