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 ! :) 
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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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 $Y(p,q) = q$. 
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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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