Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    Hi, I'm struggling to understand probability coupling. I have the following problem:

    Let X and Y each be uniformly distributed on the discrete set {1,...6} (i.e. the distribution of the roll of 1 fair die).
    (a) If X and Y are independent, what is Pr[X = Y]?
    (b) Couple X and Y so that Pr[X = Y] = 1.
    (c) Couple X and Y so that Pr[X > Y] = 5/6.

    I'm not entirely sure where to start and can't find much information on it.

    For part (b), would I be right in simply saying "Let X={1,2,...,6} and let Y={X}. Thus, Pr[X = Y] = 1." If so, great but if not where am I going wrong?

    Thanks for your help.
    Offline

    14
    ReputationRep:
    (Original post by Substitution)
    Hi, I'm struggling to understand probability coupling. I have the following problem:

    Let X and Y each be uniformly distributed on the discrete set {1,...6} (i.e. the distribution of the roll of 1 fair die).
    (a) If X and Y are independent, what is Pr[X = Y]?
    (b) Couple X and Y so that Pr[X = Y] = 1.
    (c) Couple X and Y so that Pr[X > Y] = 5/6.

    I'm not entirely sure where to start and can't find much information on it.

    For part (b), would I be right in simply saying "Let X={1,2,...,6} and let Y={X}. Thus, Pr[X = Y] = 1." If so, great but if not where am I going wrong?

    Thanks for your help.
    Is this helpful?
    Online

    20
    ReputationRep:
    Coupling?
    Offline

    14
    ReputationRep:
    (Original post by yudothis)
    Coupling?
    For example, this, I presume.
    Online

    20
    ReputationRep:
    (Original post by Gregorius)
    For example, this, I presume.
    I never knew that was called coupling :P
 
 
 
Poll
A-level students - how do you feel about your results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.