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 Snair January 8th, 2018 04:00 AM

Two random variables equal in distribution

Hi !
Can we find two random variables that are equal in distribution but are not equal ?

 Micrm@ss January 8th, 2018 04:04 AM

Of course, we can even find such variables that are independent.

The simplest example, take two similar coins. Throw them and see if you get head or tail. The distribution of the first coin will be the same as the distribution of the second. But they're surely not the same outcome.

 Snair January 8th, 2018 04:56 AM

Hi !

Quote:
 Originally Posted by Micrm@ss (Post 586832) Of course, we can even find such variables that are independent. The simplest example, take two similar coins. Throw them and see if you get head or tail. The distribution of the first coin will be the same as the distribution of the second. But they're surely not the same outcome.
Thanks for this answer. Can you tell me what are exactly the two random variables in that example ?

 Micrm@ss January 8th, 2018 10:40 AM

Let's take as sample space \$\Omega = \{(0,0), (0,1), (1,0), (1,1)\}\$, where \$0\$ is tail and \$1\$ is head.

Then we can take as variable \$X(p,q) = p\$ and \$Y(p,q) = q\$.

 Snair January 8th, 2018 02:16 PM

Hi !

Quote:
 Originally Posted by Micrm@ss (Post 586851) Let's take as sample space \$\Omega = \{(0,0), (0,1), (1,0), (1,1)\}\$, where \$0\$ is tail and \$1\$ is head. Then we can take as variable \$X(p,q) = p\$ and \$Y(p,q) = q\$.
Thanks very much. It was very useful.

 romsek January 8th, 2018 04:42 PM

as a somewhat more extreme example

suppose that the temperature in Miami is uniformly distributed between 60 and 100 degrees. (it's not but suppose it is).

and let's further suppose that the age of retirees living in Miami is also uniformly distributed between 60 and 100 yrs old.

Clearly these two random variables, temperature and age, are not equal, but they have the same distribution.

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