(a) Consider a random variable uniformly distributed between 0 and 2. Show that E(X 2 ) >...
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(a) Consider a random variable uniformly distributed between 0 and 2. Show that E(X2) > E2(X).
(b) Consider a random variable uniformly distributed between 0 and 4. Show that E(X2) > E2(X).
(c) Can you show in general that for any random variable it is true that E(X2) > E2(X) unless the random variable is zero almost always?
(Expand E {[X - E(X)]2 ≥ 0} and note that it is 0 only if X = 0 with probability 1.)
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a So it is true in this special case b So it is ...View the full answer
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Related Book For 
Principles of Communications Systems, Modulation and Noise
ISBN: 978-8126556793
7th edition
Authors: Rodger E. Ziemer, William H. Tranter
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