Which of the following statements are true and false? Prove the true ones and give counterexamples for the false ones. Let X and Z be random variables. (i) If X and Z are uncorrelated, then they are independent. (ii) If X and Z are independent, then E[X2]

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Which of the following statements are true and false? Prove the true ones and give counterexamples for the false ones. Let X and Z be random variables. (i) If X and Z are uncorrelated, then they are independent. (ii) If X and Z are independent, then E[X2]

Which of the following statements are true and false? Prove the true

ones and give counterexamples for the false ones. Let X and Z be random variables.

(i) If X and Z are uncorrelated, then they are independent.

(ii) If X and Z are independent, then E[X2] = E[Z2].

(iii) If X and Z are correlated, they are also dependent.

Bayesian

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Which of the following statements are true and false? Prove the true ones and give counterexamples for the false ones. Let X and Z be random variables. (i) If X and Z are uncorrelated, then they are independent. (ii) If X and Z are independent, then E[X2]

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Which of the following statements are true and false? Prove the true ones and give counterexamples for the false ones. Let X and Z be random variables. (i) If X and Z are uncorrelated, then they are independent. (ii) If X and Z are independent, then E[X2]