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January 8th, 2018, 04:00 AM   #1
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Two random variables equal in distribution

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

Thanks in advance !
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January 8th, 2018, 04:04 AM   #2
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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.
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January 8th, 2018, 04:56 AM   #3
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Hi !

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Originally Posted by Micrm@ss View Post
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 ?
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January 8th, 2018, 10:40 AM   #4
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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 from Snair
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January 8th, 2018, 02:16 PM   #5
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Hi !

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Originally Posted by Micrm@ss View Post
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.
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January 8th, 2018, 04:42 PM   #6
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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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