{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

STAT_333_Assignment_2 - Annotated

STAT_333_Assignment_2 - Annotated - STAT 333 Assignment 2...

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

View Full Document Right Arrow Icon
STAT 333 Assignment 2 Due: Friday, March 5 at the beginning of class 1. Suppose we toss a fair coin repeatedly. Let λ be the event “H H T T ”. a. Why is λ a renewal event? b. Use the renewal sequence { r n } to show that λ is recurrent. c. Determine ( ) R s λ (the generating function of { r n }), use it to obtain and prove recurrence. ( ) F s λ d. Use to calculate E[ T ( ) F s λ λ ]. Is λ positive recurrent or null recurrent? e. Expand in a power series and find f ( ) F s λ 8 , the probability that “H H T T” first occurs on trial 8. Give a logical explanation for this probability. f. Use the Renewal Theorem to find E[ T λ ]. Does this agree with the result in d)? 2. Suppose λ is a delayed renewal event. a. Prove the Delayed Renewal Relation: ( ) ( ) ( ) D s F s R s λ λ λ = . Hint: the proof is very similar to the proof of the Renewal Relation in class. Justify your steps carefully. b. Suppose we roll a fair six-sided die repeatedly. Let λ be the event “3 6 3”.
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