What can we say about the distribution of we have been provided the following information?

by RAHUl JHa   Last Updated January 14, 2018 13:19 PM

I have been provided the following information about the probability, then what can we say about the distribution of the random variable:

$P(X\geq\frac{1}{2}+x)=P(X\leq\frac{1}{2}+x) $

I guess the random variable follows the normal distribution but I am not able to convince myself with a formal proof of this. How can this be proved formally?



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