Question

I just need help with part C. Mostly figuring out the sketch

2·[210 total points (practice with joint, marginal and conditional densities) This is a toy problem designed to give you practice in working with a number of the concepts we've examined; in a course like this, every now and then you have to stop looking at real-world problems and just work on technique (it's similar to classical musicians needing to practice scales in addition to actual pieces of symphonic or chamber music) Suppose that the continuous random vector X = (X1, X2) has PDF given by 4x1x2 for 0 < x1 〈 1,0<T2<1 otherwise in which x = (x1,xs), and define the random vector Y = (y,Y) with the transformation (y, (a) Are X1 and X2 independent? Present any relevant calculations to support your answer. [10 points (b) Either work out the correlation ρ(Xi, X2) between X1 and X2 or explain why no calculation is necessary in correctly identifying the value of p. [10 points] (c) Sketch the set S of possible X values and the image T of S under the transformation from X to Y, and show that the joint distribution of Y-(Yİ'Y5) is otherwise in which y-(yi,Y2). Verify your calculation by demonstrating that points ' (y) dy-1. /50

Answer 1

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