{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

4703-10-Fall-h1 - IEOR 4703 HMWK 1 Professor Sigman Let U...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
IEOR 4703, HMWK 1, Professor Sigman Let U be uniformly distributed on the interval (0 , 1); P ( U x ) = x, x (0 , 1). We as- sume that your computer can sequentially generate such U independently upon demand. 1. Let X = ( b - a ) U + a . Show that X is uniformly distributed on the interval ( a, b ); that is, show that P ( X x ) = ( x - a ) / ( b - a ) , x ( a, b ). Thus, if your computer can generate a U , then it can in fact generate any rv X that is uniformly distributed on the interval ( a, b ) for any desired a and b . 2. Continuation: X has cdf given by F ( x ) = x - a b - a if x ( a, b ) , 1 if x b, 0 if x a. Show that in fact setting X = ( b - a ) U + a is exactly the inverse transform method. 3. Let V = 1 - U . Show that V is also uniformly distributed on the interval (0 , 1). (Use this fact whenever using the inverse transform method if you have a chance to replace 1 - U with U in an algorithm.) 4. Pareto distribution (power tail): Consider the cdf F ( x ) = ( 1 - 1 /x 2 if x 1 , 0 if 0 x < 1 .
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
Image of page 2
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