STAT330 Lecture Notes - Lecture 3: Xu

• School: University of Waterloo
• Department: Statistics
• Course: STAT330
• Professor: Peisong Han

Document Summary

(a) for 0 t 1, y. G (t) = p (t t) = p (x + y t) 2x (t x)2 dx =z t x4|t tx3 + For 1 t 2 we use. G (t) = p (t t) = p (x + y t) = 1 p (x + y > t) y. 2xh1 (t x)2i dx =z 1 x4|1 t 1. P (x + y > t) = z 1. Therefore the p. d. f. of t = x + y is. 3 t3 g (t) = d dt: (c) the transformation has inverse transformation. The support of the pdf for (x, y ) is. {(x, y) : 0 < x < 1, 0 < y < 1} . (cid:8)(u, v) : 0 < u < 1, = (cid:8)(u, v) : 0 < v < u, 0 < u < 1(cid:9) . U (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) g (u, v) = f(cid:0) u, v/ u(cid:1)(cid:12)(cid:12)(cid:12)(cid:12) 2v u for (u, v) ru v.