{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

FinalExam_F13 - Preliminary Exam Probability 9:00am 2:00pm...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Preliminary Exam: Probability 9:00am - 2:00pm, August 23, 2013 The exam lasts from 9:00am until 2:00pm. Your goal on this exam should be to demonstrate mastery of probability theory and maturity of thought. Your arguments should be clear, careful and complete. The exam consists of six main problems, each with several steps designed to help you in the overall solution. If you cannot justify a certain step, you still may use it in a later step. On you work, label the steps this way: (i), (ii),... On each page you turn in, write your assigned code number instead of your name. Separate and staple each main part and return each in its designated folder.
Image of page 1

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

View Full Document Right Arrow Icon
Problem 1 (14 pts) . Let be a random variable and denote ( ) . Let be independent and identically distributed random variables and denote , a. (8 points) (i). Let be a real number. Prove that for each we have . (ii). Show how to modify the LHS of the inequality so that it will hold, with the same RHS, for .
Image of page 2
Image of page 3
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