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 < ∞ ]******PART B. Identify the marginal distributions of X and Y by type and parameter values.****** (Please help with this part). 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? Using part d if possible or else directly from your joint probability table: Comptue E[XY] and then the correlation rX,Y = COV(X,Y)/ [sX*sY].

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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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 < ∞ ]

******PART B. Identify the marginal distributions of X and Y by type and parameter values.****** (Please help with this part).

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? Using part d if possible or else directly from your joint probability table: Comptue E[XY] and then the correlation r_X,Y = COV(X,Y)/ [s_X*s_Y].

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