The joint continuous distribution of random variables X and Y is given byf X,Y(x,y) = l2exp[-lx] for 0 < y < x < ∞ for some parameter l >0. = l2exp[-lx] * I[ 0 < y < x < ∞ ]Are X and Y independent? Explain.Identify the marginal distributions of X and Y by type and parameter values. Now assume that l = 3 to do the numeric computations in parts c and d.Using your findings in part b. you can simply state the means E[X] and E[Y] and variances VAR[X] and VAR[Y]. (to be used below in CORR(X,Y))Using part b, Can you state the conditional expectation E[Y | X =x] for all possible values x of X?

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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The joint continuous distribution of random variables X and Y is given by

f_X,Y(x,y) = l²exp[-lx] for 0 < y < x < ∞ for some parameter l >0.

= l²exp[-lx] * I[ 0 < y < x < ∞ ]

Are X and Y independent? Explain.
Identify the marginal distributions of X and Y by type and parameter values.

Now assume that l = 3 to do the numeric computations in parts c and d.

Using your findings in part b. you can simply state the means E[X] and E[Y] and variances VAR[X] and VAR[Y]. (to be used below in CORR(X,Y))
Using part b, Can you state the conditional expectation E[Y | X =x] for all possible values x of X?

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E[X] and E[Y] and variances VAR[X] and VAR[Y]. (to be used below in CORR(X,Y)) Using part b, Can you state the conditional expectation E