Recall that we say that a random variable X is in the vector space L^2 if it has finite second moment, EX^2 In this problem we will understand a bit better the geometry of the vector space L^2(1) Show that ||X||_2 = √EX^2 is a norm

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Recall that we say that a random variable X is in the vector space L^2 if it has finite second moment, EX^2 In this problem we will understand a bit better the geometry of the vector space L^2
(1) Show that ||X||_2 = √EX^2 is a norm

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