Is there a random variable X such that
E[X^2]=E[X]^2?

if yes, is it self-independent ?

Question

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

anonymous · Answer

this really seems like an interesting question, but maybe you can make it clearer, are you sure this is the right question?

anonymous · Answer

yes

anonymous · Answer

is E[x} the exponential function

anonymous · Answer

i tought that Var(x)=E[X^2]-E[X]^2 , so for Var(X)=0 E[X^2]=E[X]^2

anonymous · Answer

no E[X] is the expectation of x

anonymous · Answer

oh im sorry

anonymous · Answer

so based on my reasing then I have to find a random variable for which the Var(x)=0, i think

anonymous · Answer

?

anonymous · Answer

if X is Cauchy Distributed then this will be true..., you can have the standardized Cauchy dist. 1/(pi*(1+(x^2)))

valpey · Answer

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).