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Is there a random variable X such that E[X^2]=E[X]^2? if yes, is it self-independent ?

Probability
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this really seems like an interesting question, but maybe you can make it clearer, are you sure this is the right question?
yes
is E[x} the exponential function

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i tought that Var(x)=E[X^2]-E[X]^2 , so for Var(X)=0 E[X^2]=E[X]^2
no E[X] is the expectation of x
oh im sorry
so based on my reasing then I have to find a random variable for which the Var(x)=0, i think
?
if X is Cauchy Distributed then this will be true..., you can have the standardized Cauchy dist. 1/(pi*(1+(x^2)))
Hard to call a variable "random" if it doesn't vary. It is also hard to show that this is true for the standardized Cauchy Distribution (basically a distribution with significant probability weight at (+/-)1/0).

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