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(Solved) : 7 Independence Let U 0 1 5 R Random Variable Uniform U Define Following Random Variables X Q44054955 . . .

7. [Independence] Let U = {0,1}5 and R be a random variable uniform over U. Define the following random variables: X = Isb3(R) and Y=msb3(R), where “Isb;” denotes 3 least significant bits and “msb;” denotes 3 most significant bits. Are X and Y independent or not? Argue your answer formally using the definition of independence. [15 points] Show transcribed image text 7. [Independence] Let U = {0,1}5 and R be a random variable uniform over U. Define the following random variables: X = Isb3(R) and Y=msb3(R), where “Isb;” denotes 3 least significant bits and “msb;” denotes 3 most significant bits. Are X and Y independent or not? Argue your answer formally using the definition of independence. [15 points]

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Answer to 7. [Independence] Let U = {0,1}5 and R be a random variable uniform over U. Define the following random variables: X = I…