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Suppose that the random variables Y1 and Y2 have joint probability density function f(y1, y2) given by f(y1, y2)={ 6 y1^2 y2, 0 ≤ y1≤ y2, y1 y2≤ 2 0, elsewhere. a. Verify that this is a valid joint density function. b. What is the probability that Y1 Y2 is less than 1 ? | Numerade
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Let Y1 and Y2 have the joint probability density function given by: f(y1, y2) = (6(1 − y2), if 0 ≤ y1 ≤ y2 ≤ 1; 0, elsewhere.i) Find marginal density fY1 of Y1 and marginal density fY2 of Y2.ii) Find Cov(Y1, Y2). Based on the value of the covariance, are Y1 and Y2 independent?iii) Find E(Y1 − 3Y2) and Var(Y1 − 3Y2).iv) Find the correlation coefficient ρY1,Y2 of random variables Y1 and Y2.
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