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# Probability coupling watch

1. 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?

2. (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?

3. Coupling?
4. (Original post by yudothis)
Coupling?
For example, this, I presume.
5. (Original post by Gregorius)
For example, this, I presume.
I never knew that was called coupling :P

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