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  3. 1 let x and y be two independent random variables...

Question: 1 let x and y be two independent random variables...

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1. Let X and Y be two independent random variables following beta distributions Beta(120, 2019) (a) Whats P(X 0.3)? (b) Whats E(2X - Y)? (c) Whats P(2X +4 > 3Y)? (d) Whats P(X < Y)? (e) Now if X and Y are no longer independent to each other. Will the answers to a)-(d) remain the same? Explain. (f) Now define Z~Beta(2019, 120). Compare the median of X and Z, which one is bigger? Compare the variance of X and Z, which one is bigger? Explain (Hint: no calculation is needed)
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