Question 3 Consider the random variable (X,Y) which has density Sk (r,y) ET, f(x,y)(x,y) = 10 otherwise where T is the t

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Question 3 Consider The Random Variable X Y Which Has Density Sk R Y Et F X Y X Y 10 Otherwise Where T Is The T 1 (41.74 KiB) Viewed 22 times

Question 3 Consider the random variable (X,Y) which has density Sk (r,y) ET, f(x,y)(x,y) = 10 otherwise where T is the triangle {(x,y): r >0, y > 0,x+y <9}. (a) What is the value of k? (b) Explain why X and Y are dependent (no calculations should be required). Page 6 of 8 pages MAST20004 Probability Semester 1 (c) Find fy(y), the marginal pdf of Y. Check that it is a probability density (d) For a fixed y € (0.9) write down the set of values of 1 for which fxY=y(xly) is non-zero. (e) Find fx Y=y(|y) over the range that you derived in part (d).