Question 24. (a) Prove that if two continuous random variables X and Y are independent, then the expected value of the product, E(XY) is the product of the marginal expectations. Start the proof with the definition of E(XY). (b) Prove that if two random variables X andY are independent, so are the following functions of the two random variables W = a + bX and T = c + dY. You may use just the expectation operator and the result obtained in part (a).

Question 24. (a) Prove that if two continuous random variables X and Y are independent, then the expected value of the product, E(XY) is the product of the marginal expectations. Start the proof with the definition of E(XY). (b) Prove that if two random variables X andY are independent, so are the following functions of the two random variables W = a + bX and T = c + dY. You may use just the expectation operator and the result obtained in part (a).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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