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c. Suppose that the random variables X1, X2 and X3 are independent with means and variances as follows: Hi = 8 of = 36 H2 = 5 o = 81 H3 = 7 o = 49 Let Y1 = X1 +2X2 and Y2 = 2.X1 – }X2 – X3. (i) Find the Cov(Y1, Y2). (ii) Assuming that X1, X2 and X3 are Normal random variables, calculate P(Y < 2Y;).

c. Suppose that the random variables X1, X2 and X3 are independent with means and variances as follows: Hi = 8 of = 36 H2 = 5 o = 81 H3 = 7 o = 49 Let Y1 = X1 +2X2 and Y2 = 2.X1 – }X2 – X3. (i) Find the Cov(Y1, Y2). (ii) Assuming that X1, X2 and X3 are Normal random variables, calculate P(Y < 2Y;).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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c. Suppose that the random variables X1, X2 and X3 are independent with means and variances as follows: H1 = 8 of = 36 H2 = 5 o = 81 H3 = 7 o3 = 49 Let Y1 = X1 + 2X, and Y2 = 2X1 – }X2 – X3. (i) Find the Cov(Y1, Y2). (ii) Assuming that X1, X2 and X3 are Normal random variables, calculate P(Y < 2Y,).
Transcribed Image Text:c. Suppose that the random variables X1, X2 and X3 are independent with means and variances as follows: H1 = 8 of = 36 H2 = 5 o = 81 H3 = 7 o3 = 49 Let Y1 = X1 + 2X, and Y2 = 2X1 – }X2 – X3. (i) Find the Cov(Y1, Y2). (ii) Assuming that X1, X2 and X3 are Normal random variables, calculate P(Y < 2Y,).
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